Daily Papers

Existing RL post-training methods for text-to-image generation usually convert the final-image reward into a single scalar advantage and apply it with the same strength to the entire generative trajectory. However, text-to-image generation naturally has temporal and spatial structure: different denoising steps are responsible for different generation stages, and the content that truly determines text alignment often appears only in part of the image. This granularity mismatch makes it difficult for policy updates to focus on the generative components that actually affect the reward. To address this issue, we propose SpatioTemporal Adaptive Reward (STAR) Allocation for RL post-training of text-to-image diffusion and flow models. STAR uses text-image attention inside the generative model and starts from the core content that the user truly cares about in the prompt. It constructs spatial allocation maps that dynamically vary across denoising steps and rollouts, and allocates the same group-relative advantage to more relevant latent regions with almost no additional computational overhead. STAR then applies stronger policy updates to these regions through a spatially resolved policy objective. We use Stable Diffusion 3.5 Medium as the base model and evaluate on three tasks: GenEval, OCR text rendering, and PickScore. Experimental results show that STAR improves compositional semantic alignment, text rendering, and preference optimization without changing the external reward source, achieving 0.9759, 0.9757, and 23.60 on GenEval, OCR, and PickScore, respectively.

Reinforcement Learning with Verifiable Rewards (RLVR) has catalyzed significant advances in the reasoning capabilities of Large Language Models (LLMs). However, effectively managing the exploration and exploitation trade-off remains a critical challenge. In this paper, we fully analyze the exploration and exploitation dilemma of extremely hard and easy samples during the training and propose a new fine-grained trade-off mechanism. Concretely, we introduce a perplexity space disentangling strategy that divides the sample space into distinct exploration (high perplexity) and exploitation (low perplexity) subspaces, thereby mining fine-grained samples requiring exploration-exploitation trade-off. Subsequently, we propose a bidirectional reward allocation mechanism with a minimum impact on verification rewards to implement perplexity-guided exploration and exploitation, enabling more stable policy optimization. Finally, we have evaluated our method on two mainstream tasks: mathematical reasoning and function calling, and experimental results demonstrate the superiority of the proposed method, confirming its effectiveness in enhancing LLM performance by fine-grained exploration-exploitation trade-off.

We consider a project (model) owner that would like to train a model by utilizing the local private data and compute power of interested data owners, i.e., trainers. Our goal is to design a data marketplace for such decentralized collaborative/federated learning applications that simultaneously provides i) proof-of-contribution based reward allocation so that the trainers are compensated based on their contributions to the trained model; ii) privacy-preserving decentralized model training by avoiding any data movement from data owners; iii) robustness against malicious parties (e.g., trainers aiming to poison the model); iv) verifiability in the sense that the integrity, i.e., correctness, of all computations in the data market protocol including contribution assessment and outlier detection are verifiable through zero-knowledge proofs; and v) efficient and universal design. We propose a blockchain-based marketplace design to achieve all five objectives mentioned above. In our design, we utilize a distributed storage infrastructure and an aggregator aside from the project owner and the trainers. The aggregator is a processing node that performs certain computations, including assessing trainer contributions, removing outliers, and updating hyper-parameters. We execute the proposed data market through a blockchain smart contract. The deployed smart contract ensures that the project owner cannot evade payment, and honest trainers are rewarded based on their contributions at the end of training. Finally, we implement the building blocks of the proposed data market and demonstrate their applicability in practical scenarios through extensive experiments.

Multimodal Large Language Models (MLLMs) have demonstrated remarkable capabilities in emotional intelligence. However, prevailing research predominantly focuses on task-specific specialization, often neglecting inter-task synergy and leaving latent reasoning potential underexplored. To bridge this gap, we introduce OneEmo, a unified affective generalist capable of mastering emotion perception, comprehension, and interaction. For this purpose, we first construct EmoWorld-130K, a comprehensive dataset that distills specialized affective knowledge into explicit reasoning trajectories via a human-in-the-loop workflow. Supervised fine-tuning on this corpus reveals significant mutual benefits derived from multi-task learning. Second, to fully unlock the latent reasoning potential, we propose Emo-Chord, a novel reinforcement learning strategy that stabilizes optimization through unified multi-task reward allocation. Extensive experiments demonstrate that OneEmo achieves state-of-the-art performance against similarly sized baselines across most benchmarks. Notably, despite having significantly fewer parameters than commercial models, OneEmo delivers highly competitive results. This paper paves the way for more reliable and interpretable affective computing. The code is available at https://github.com/waHAHJIAHAO/OneEmo.

Group Relative Policy Optimization (GRPO) has advanced generative model post-training in verifiable domains such as code and mathematics, but evaluating video quality, especially emotional expression, often depends on subjective aesthetics and has no uniquely correct target. Existing approaches typically rely on fixed rewards for visual quality, motion quality, and text alignment that poorly capture emotional intent and can invite reward hacking, while RLHF is difficult to scale and subject to individual aesthetic differences that complicate the calibration of facial, body motion, and chromatic cues across narrative contexts. We introduce EmoReward, a new self-evolving training mechanism that distills evidence reliability from reward traces collected during an actual training run to adaptively guide multi-reward weight allocation in subsequent training by determining which emotional evidence to trust and how much to weight it. EmoReward first plans specific grounding cues from the emotional prompt to guide evaluation, then uses heterogeneous signal primitives to score the generated video during the act stage. Reflective Reward Gating calibrates their contributions through instance-level gates for phase, face confidence, conflict, and subtlety, then renormalizes weights over the active set to produce the sample's fused reward. RewardMemory then estimates each primitive's reliability from rollout scores and outcomes within each emotional regime in the finished training run, then fixes bounded multipliers that calibrate fusion weights in the next training run without updating reward models. Experiments on HunyuanVideo 1.5 show improvements across multiple RL algorithms and compare EmoReward with other agentic reward methods under SAGE-GRPO. Ablations and transfer experiments on SD 3.5 and FLUX further support adaptive reward calibration for visual generation.

Multimodal Large Language Models (MLLMs) show strong visual perception, yet remain limited in reasoning about space under changing viewpoints. We study this challenge as Perspective-Conditioned Spatial Reasoning (PCSR) in 360-degree omnidirectional images, where broad scene coverage reduces ambiguity from partial observations without eliminating the need for viewpoint-dependent inference. To assess this capability, we introduce PCSR-Bench, a diagnostic benchmark of 84,373 question-answer pairs from 2,600 omnidirectional images across 26 indoor environments. PCSR-Bench contains eight tasks spanning foundational perception (e.g., object counting, relative distance, and relative direction) and advanced PCSR, including compositional chains, egocentric rotation, perspective re-anchoring, ego-distortion, and limited-FOV visibility. We evaluate 14 representative MLLMs and observe a substantial perception-reasoning gap: accuracy reaches 57.59% on foundational relative direction, but drops to 13.49% on egocentric rotation, 7.13% on egocentric distortion, and 0.64% on open-ended compositional reasoning. To probe the plasticity of this gap, we conduct an RL-based diagnostic study on a 7B-scale model. Reward shaping improves a matched 7B baseline from 31.10% to 60.06% under a controlled setting, suggesting that PCSR is partial plasticity rather than being fully immutable. Still, the gains are task-selective, sensitive to reward design including both weight allocation and reward formulation, and partially dependent on the evaluation protocol. These results position PCSR as a key bottleneck in current MLLMs and highlight limited but meaningful room for recovery under targeted optimization.

In settings where labeled verifiable training data is the binding constraint, each checked example should be allocated carefully. The standard practice is to use this data directly on the model that will be deployed, for example by running GRPO on the deployment student. We argue that this is often an inefficient allocation because it overlooks a reward-density principle: sparse sequence-level reward should train models where exploration is productive, while dense token-level teacher reward should be used where the aim is to compress behavior into a smaller model. In this view, GRPO-style sparse RL and OPD-style dense teacher supervision are not separate recipes; they are different reward-density regimes. The allocation rule is simple: use scarce labeled training data upstream on the strongest model that can turn it into reward-shaped behavior, then transfer that behavior downstream as dense supervision. We evaluate this rule on verifiable math with Qwen3 and Llama models. At fixed Qwen3-1.7B deployment-student size, an RL-improved 8B teacher distilled through the dense bridge outperforms direct GRPO on the same student, while transfer from the same teacher before RL underperforms. The bridge is important: a forward-KL warmup on teacher rollouts followed by OPD on student rollouts is consistently strongest on MATH before any post-bridge student-side sparse RL, and also gives the best pre-Stage~3 AIME endpoints for the canonical 8B/14B teachers. The bridge also makes later student-side sparse RL effective: GRPO that is weak on a cold student lifts MATH from 75.4% to 78.5% after the bridge and outperforms a matched replay control by 2.8 points. The operational principal is to avoid using scarce labeled data on the least prepared policy: use sparse reward for teacher-side discovery, dense transfer for student compression, and student-side sparse reward only after the bridge.

Training diffusion models with multiple rewards requires distinguishing user preference from reward informativeness. User preference determines how much each reward should contribute to the overall objective; reward informativeness determines when its feedback is useful during denoising. Some rewards can meaningfully evaluate a sample as soon as global structure emerges, but others become informative only when the sample is nearly clean. To address both questions jointly, we propose ReCAST (Reward Credit ASsignment across T}imesteps), the first method, to our knowledge, for per-reward, timestep-dependent credit assignment in diffusion reward fine-tuning. ReCAST separates user preferences from temporal allocation through a reward-by-timestep weight matrix W, whose row sums match the user-specified reward budgets λ, while its column sums are equal, assigning the same total weight to each denoising step. Under these marginal constraints, ReCAST allocates weight according to each reward's informativeness, quantified by its Rényi discriminability gain at each step. These gains telescope to the total discriminability between the reward-induced positive policy and the current policy, providing a basis for temporal credit assignment. We evaluate ReCAST by training SD3.5-Medium under two distinct four-reward settings, each across five reward budgets λ. ReCAST improves the training rewards in one setting and matches them in the other, improves every held-out judge in both, and is preferred by an independent LLM-as-a-Judge. Together, these results show that ReCAST yields improvements that generalize beyond the training rewards and support its core principle: assigning each reward greater weight at the denoising timesteps where its feedback is most informative.

Large Language Models (LLMs) have achieved significant advances in reasoning tasks. A key approach is tree-based search with verifiers, which expand candidate reasoning paths and use reward models to guide pruning and selection. Although effective in improving accuracy, these methods are not optimal in terms of efficiency: they perform simple decomposition on the reasoning process, but ignore the planning-execution nature of tasks such as math reasoning or code generation. This results in inefficient exploration of reasoning process. To address this, we propose a dual-phase test-time scaling framework that explicitly separates reasoning into planning and execution, and performs search over the two phases individually. Specifically, we decompose reasoning trajectories and develop reward models for each phase, enabling the search to explore and prune plans and executions separately. We further introduce a dynamic budget allocation mechanism that adaptively redistributes sampling effort based on reward feedback, allowing early stopping on confident steps and reallocation of computation to more challenging parts of the reasoning process. Experiments on both mathematical reasoning and code generation benchmarks demonstrate that our approach consistently improves accuracy while reducing redundant computation.

Complex reinforcement learning environments frequently employ multi-task and mixed-reward formulations. In these settings, heterogeneous reward distributions and correlated reward dimensions often destabilize the construction of scalar advantages. To address these challenges, we propose Reward-Decorrelated Policy Optimization (RDPO), a reward-processing method designed to explicitly target both failure modes. RDPO first utilizes Magnitude-Aware Quantile normalization to stabilize prompt-level advantage allocation across binary, fractional, and continuous rewards. It then applies Mahalanobis whitening within each active reward subspace to mitigate correlation redundancy prior to aggregation. When applied during the post-training of LongCat-Flash, RDPO enhances instruction following, writing quality, and robustness to hard prompts while remaining broadly competitive on reasoning and coding evaluations.

Reinforcement learning with verifiable rewards (RLVR) is a promising approach for enhancing reasoning and agentic behavior in large language models. However, rollout-intensive policy optimization is often limited by insufficient reward contrast, arising when overly simple or complex prompts generate low-variance feedback and when outcome-only rewards assign the same terminal assessment to every decision in a multi-turn rollout. Past efforts have focused on allocating available rollout resources to promising prompts, yet they only leverage sample informativeness at the prompt level and neglect variation in prefix-level informativeness across turns within the same rollout. This work targets multi-turn agentic RL by modeling each ReAct-style thought-action-observation turn as a semantically distinct node, allowing budget allocation to extend from prompt roots to turn-level prefixes with further continuations, which naturally forms tree-structured rollouts. We introduce Tree Rollout Allocation for Contrastive Exploration (TRACE), a unified rollout allocation framework that enhances reward contrast within a fixed sampling budget. Technically, TRACE allocates rollout budget to both prompt roots and intermediate prefixes that are most likely to yield mixed terminal rewards. A shared generalizable predictor estimates conditional success probability at these anchors from prefix histories to guide this allocation. The resulting adaptive tree structure enriches outcome-only feedback and amplifies the policy-update signal. Empirically, TRACE achieves competitive performance and efficiency gains on typical agentic benchmarks, e.g., improving Qwen3-14B Multi-Hop QA average accuracy by 2.8 points over competitive baselines at equal sampling cost.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a highly effective framework for improving LLM reasoning, with methods such as GRPO among its most successful instantiations. However, GRPO relies on repeated generation of long chain-of-thought rollouts. Training time scales with the number of rollouts, a large fraction of which are uninformative. Thus, GRPO is computationally expensive and unstable. To mitigate this, existing approaches either generate a larger pool of rollouts and filter the most informative prompts, or leverage historical signals for filtering at later stages of training. These strategies offer modest performance gains, but slow down the overall process. To address this, we propose VarIance Guided Online Rollout allocation (VIGOR) which instead of allocating a fixed rollout budget per example, begins with a small number of rollouts for all examples in a batch and iteratively allocates additional rollouts to those with the highest group reward variance until a fixed total rollout budget is reached. Theoretically, we show that under RLVR, reward variance controls the gradient magnitude, and derive VIGOR's closed-form speedup ratio over GRPO, which grows with refinement rounds under Pareto-distributed reward variance. Experiments on mathematical reasoning and coding tasks show that VIGOR reaches target accuracy with up to 2.3times fewer rollouts on math, reaches GRPO's final coding full pass rate with 1.49times fewer rollouts, and improves the coding average test pass rate by 3.4 points.

Autonomous research agents aim to automate scientific workflows, from proposing ideas to conducting experiments and analyzing results. Yet current AI and research agents can propose more directions than available resources allow them to pursue. Moreover, each attempt could consume substantial resources, requiring agents to reconsider how to invest in subsequent research. Thus, deciding how to invest research effort strategically should be a defining capability of autonomous research agents. Accordingly, we introduce PrimeScientist, which jointly determines research direction and resource investment across successive research attempts. Specifically, we formulate this challenge of strategic research effort allocation as a sequential decision problem where remaining resources should explicitly guide the research policy. We first introduce an executable plan tree that preserves competing plans and their outcomes across attempts. Building on this representation, we propose an adaptive MCTS-based allocation policy that balances exploration and exploitation using experimental feedback and remaining resources. Comprehensive evaluations across AI research, systems and code optimization, and machine learning engineering show that strategic allocation improves research quality and sample efficiency together. Across 12 AI research tasks, PrimeScientist improves average reward by 10.3% with 50.6% fewer research attempts than AutoResearch under the same resource budget. We believe making research effort allocation an explicit optimization target establishes effective resource use as a core research capability for autonomous agents to drive scientific breakthroughs at scale.

In the context of a short video & live stream mixed recommendation scenario, the live stream recommendation system (RS) decides whether to allocate at most one live stream into the video feed for each user request. To maximize long-term user engagement, it is crucial to determine an optimal live stream policy for accurate live stream allocation. The inappropriate live stream allocation policy can significantly affect the duration of the usage app and user retention, which ignores the long-term negative impact of live stream allocation. Recently, reinforcement learning (RL) has been widely applied in recommendation systems to capture long-term user engagement. However, traditional RL algorithms often face divergence and instability problems, which restricts the application and deployment in the large-scale industrial recommendation systems, especially in the aforementioned challenging scenario. To address these challenges, we propose a novel Supervised Learning-enhanced Multi-Group Actor Critic algorithm (SL-MGAC). Specifically, we introduce a supervised learning-enhanced actor-critic framework that incorporates variance reduction techniques, where multi-task reward learning helps restrict bootstrapping error accumulation during critic learning. Additionally, we design a multi-group state decomposition module for both actor and critic networks to reduce prediction variance and improve model stability. We also propose a novel reward function to prevent overly greedy live stream allocation. Empirically, we evaluate the SL-MGAC algorithm using offline policy evaluation (OPE) and online A/B testing. Experimental results demonstrate that the proposed method not only outperforms baseline methods under the platform-level constraints but also exhibits enhanced stability in online recommendation scenarios.

Chinese Semantic Error Correction (CSEC) targets semantic errors in Chinese text, which are typically more subtle and complex than spelling and grammatical errors but remain relatively underexplored. Existing LLM-based approaches face two recurring obstacles in this task: over-correction, and unclear interaction between Chain-of-Thought (CoT) reasoning and self-consistency decoding, such that the benefits brought by CoT cannot be reliably transferred to final corrections. We propose Vote-guided Advantage Allocation for CSEC (VAA-CSEC), a multi-stage framework that combines CoT distillation, Supervised Fine-Tuning (SFT), Reinforcement Learning (RL) and self-consistency decoding. During RL, we design a task-specific reward function that directly aligned with the minimal-editing principle of CSEC. We further introduce Group-Level Relative Policy Optimization (GLPO), which reallocates GRPO advantages according to the margin between individual rollout rewards and the vote-aggregated group reward, aligning the RL training objective with the self-consistency objective used at inference time. Experiments on CSED-C and NaSGEC-Exam show that VAA-CSEC outperforms all LLM-based baselines on CSED-C with an F0.5 of 47.72%, achieves the highest recall of 42.15% among all methods, and establishes a new state of the art of 41.55% F0.5 on NaSGEC-Exam.

Computationally intensive decoding procedures--including search, reranking, and self-critique--can improve the quality of language model (LM) outputs in problems spanning code generation, numerical reasoning, and dialog. Existing work typically applies the same decoding procedure for every input to an LM. But not all inputs require the same amount of computation to process. Can we allocate decoding computation adaptively, using more resources to answer questions whose answers will be harder to compute? We present an approach that predicts the distribution of rewards given an input and computation budget, then allocates additional computation to inputs for which it is predicted to be most useful. We apply this approach in two decoding procedures: first, an adaptive best-of-k procedure that dynamically selects the number of samples to generate as input to a reranker; second, a routing procedure that dynamically responds to a query using a decoding procedure that is expensive but accurate, or one that is cheaper but less capable. Across a suite of programming, mathematics, and dialog tasks, we show that accurate computation-allocation procedures can be learned, and reduce computation by up to 50% at no cost to response quality, or improve quality by up to 10% at a fixed computational budget.

Reinforcement learning (RL) is the dominant paradigm for post-training large language models. However, in the online, on-policy setting, rollout generation dominates the computational cost of training. Group-based policy optimization methods compute advantages from multiple rollouts per prompt, yet they indiscriminately allocate budget to prompts with collapsed reward distributions, wasting expensive rollouts on negligible learning signals. We demonstrate that group-based updates are most effective in regimes of high reward variance. Since the policy evolves throughout training, prompt informativeness must be estimated online rather than precomputed, but exhaustively evaluating every prompt is computationally prohibitive. We introduce Pilot-Commit, a budget-aware rollout allocation framework for group-based RL post-training. Pilot-Commit decouples prompt evaluation from exploitation: a pilot stage estimates per-prompt informativeness using a fraction of the budget, and the remaining rollouts are allocated to high-leverage prompts while low-signal prompts are skipped. Across multiple math reasoning benchmarks and model scales from 1.5B to 14B parameters, Pilot-Commit matches baseline accuracy with significantly lower sampling costs, reaching target accuracy up to 1.9times faster than GRPO and 4.0times faster than DAPO in cumulative rollouts.

Neurosymbolic systems rely on mathematical solvers to guarantee reasoning correctness, yet solvers are fundamentally blind to whether a formal translation maintains strict reference-equivalence to a designated formalization. We formalize this vulnerability as Verdict-Preserving-Unfaithfulness (VPU): a failure mode where an incorrect encoding executes successfully and matches the expected verdict. We theoretically prove that structural, verdict-only verification heuristics are mathematically bounded to chance-level detection on these deceptively valid traces. To resolve this, we introduce Generative Verification (GenV), which distills an offline Z3-equivalence oracle into a reference-free, continuous reference-equivalence score by repurposing the language model's native vocabulary space. Mechanistic analysis via decision-projected logit lenses and sparse autoencoders shows this generative readout natively extracts precise spatial error coordinates without explicit localization training. Empirically, our oracle-mined verifier (GenV+HN) achieves 0.961 AUROC in reference-equivalence verification, generalizes zero-shot across unseen translators and divergent formal styles, and yields an 11.3-point downstream accuracy gain in agentic test-time compute allocation.

Online allocation problems with resource constraints are central problems in revenue management and online advertising. In these problems, requests arrive sequentially during a finite horizon and, for each request, a decision maker needs to choose an action that consumes a certain amount of resources and generates reward. The objective is to maximize cumulative rewards subject to a constraint on the total consumption of resources. In this paper, we consider a data-driven setting in which the reward and resource consumption of each request are generated using an input model that is unknown to the decision maker. We design a general class of algorithms that attain good performance in various input models without knowing which type of input they are facing. In particular, our algorithms are asymptotically optimal under independent and identically distributed inputs as well as various non-stationary stochastic input models, and they attain an asymptotically optimal fixed competitive ratio when the input is adversarial. Our algorithms operate in the Lagrangian dual space: they maintain a dual multiplier for each resource that is updated using online mirror descent. By choosing the reference function accordingly, we recover the dual sub-gradient descent and dual multiplicative weights update algorithm. The resulting algorithms are simple, fast, and do not require convexity in the revenue function, consumption function and action space, in contrast to existing methods for online allocation problems. We discuss applications to network revenue management, online bidding in repeated auctions with budget constraints, online proportional matching with high entropy, and personalized assortment optimization with limited inventory.

Efficient downlink radio resource management in 5G requires jointly optimizing user scheduling and transmit-power allocation under time-varying wireless conditions. This is challenging in OFDMA systems because PRB assignment is combinatorial, power allocation is continuous, and performance depends on channel evolution, link adaptation, and long-term fairness. We propose a hierarchical cooperative multi-agent reinforcement learning framework with staged curriculum training for joint downlink PRB and power allocation in a physically grounded 5G environment. System-level simulation is implemented in Sionna, while Sionna RT supports wireless scene construction and mobility-aware ray-traced channel generation. The control task is decomposed into two sequential stages: a PRB agent learns user-level resource shares, which are converted to exact PRB assignments by a deterministic channel-aware quota resolver, and a power agent distributes the base-station power budget across users and their assigned PRB-symbol resources. The framework operates in a cross-layer loop with adaptive modulation and coding, HARQ feedback, outer-loop link adaptation, and a fairness-aware reward based on smoothed throughput and Jain's fairness index. Training stability is improved through a three-phase curriculum for PRB allocation, power control, and joint fine-tuning. Under matched channel realizations, we compare against a PF scheduler with equal-power transmission and two ablations isolating the learned PRB and power-control components. Results show that both learned components improve throughput distribution relative to PF, while the full PRB and power controller achieves the largest cell-throughput gain with only a modest reduction in Jain's fairness index.

Public service systems in many African regions suffer from delayed emergency response and spatial inequity, causing avoidable suffering. This paper introduces OPTIC-ER, a reinforcement learning (RL) framework for real-time, adaptive, and equitable emergency response. OPTIC-ER uses an attention-guided actor-critic architecture to manage the complexity of dispatch environments. Its key innovations are a Context-Rich State Vector, encoding action sub-optimality, and a Precision Reward Function, which penalizes inefficiency. Training occurs in a high-fidelity simulation using real data from Rivers State, Nigeria, accelerated by a precomputed Travel Time Atlas. The system is built on the TALS framework (Thin computing, Adaptability, Low-cost, Scalability) for deployment in low-resource settings. In evaluations on 500 unseen incidents, OPTIC-ER achieved a 100.00% optimality rate with negligible inefficiency, confirming its robustness and generalization. Beyond dispatch, the system generates Infrastructure Deficiency Maps and Equity Monitoring Dashboards to guide proactive governance and data-informed development. This work presents a validated blueprint for AI-augmented public services, showing how context-aware RL can bridge the gap between algorithmic decision-making and measurable human impact.

Artificial intelligence is transforming financial investment decision-making frameworks, with deep reinforcement learning demonstrating substantial potential in robo-advisory applications. This paper addresses the limitations of traditional portfolio optimization methods in dynamic asset weight adjustment through the development of a deep reinforcement learning-based dynamic optimization model grounded in practical trading processes. The research advances two key innovations: first, the introduction of a novel Sharpe ratio reward function engineered for Actor-Critic deep reinforcement learning algorithms, which ensures stable convergence during training while consistently achieving positive average Sharpe ratios; second, the development of an innovative comprehensive approach to portfolio optimization utilizing deep reinforcement learning, which significantly enhances model optimization capability through the integration of random sampling strategies during training with image-based deep neural network architectures for multi-dimensional financial time series data processing, average Sharpe ratio reward functions, and deep reinforcement learning algorithms. The empirical analysis validates the model using randomly selected constituent stocks from the CSI 300 Index, benchmarking against established financial econometric optimization models. Backtesting results demonstrate the model's efficacy in optimizing portfolio allocation and mitigating investment risk, yielding superior comprehensive performance metrics.

Process Reward Models (PRMs) provide step-level feedback for reasoning, but current PRMs usually output only a single reward score for each step. Downstream methods must therefore treat imperfect step-level reward predictions as reliable decision signals, with no indication of when these predictions should be trusted. We propose BetaPRM, a distributional PRM that predicts both a step-level success probability and the reliability of that prediction. Given step-success supervision from Monte Carlo continuations, BetaPRM learns a Beta belief that explains the observed number of successful continuations through a Beta-Binomial likelihood, rather than regressing to the finite-sample success ratio as a point target. This learned reliability signal indicates when a step reward should be trusted, enabling downstream applications to distinguish reliable rewards from uncertain ones. As one application, we introduce Adaptive Computation Allocation (ACA) for PRM-guided Best-of-N reasoning. ACA uses the learned reliability signal to stop when a high-reward solution is reliable and to spend additional computation on uncertain candidate prefixes. Experiments across four backbones and four reasoning benchmarks show that BetaPRM improves PRM-guided Best-of-N selection while preserving standard step-level error detection. Built on this signal, ACA improves the accuracy--token tradeoff over fixed-budget Best-of-16, reducing token usage by up to 33.57% while improving final-answer accuracy.

Multi-agent systems promise a new axis for scaling inference: rather than having one agent think longer or sample more attempts, a task is split across many agents that work in parallel and coordinate. However, in practice, more agents can easily produce duplicate work, coordination failures, and higher costs. We therefore formulate team design as a compute allocation problem: starting from a solo agent, where should additional inference compute go to reach the reward-cost Pareto frontier? We build a minimal multi-agent harness from the ground up and trace this frontier by varying, one at a time, the workflow stage at which a lead delegates to its workers (planning, implementation, or verification), the models that form the team, and the number of workers. On ProgramBench, teams outperform solo agents but cost three to seven times as much. With the right compute allocation, however, a heterogeneous 17-agent team comes within 1.4 points of a strong homogeneous 5-agent team at 70% lower cost. This efficiency stems from three findings. First, planning is the most valuable use of workers: in a homogeneous team whose lead decides how many workers to spawn, a lead that delegates only planning to its workers, and then implements and verifies the code itself, matches the reward of a lead that delegates to workers throughout planning, implementation, and verification, at half the cost. Second, cheap models pay off as planners but not as implementers: a strong lead with cheap planners recovers 47.5% of the reward gain of an all-strong team for only 13.9% of its additional cost, whereas cheap implementers lower reward. Third, planners keep improving reward as the team grows, whereas implementers and verifiers plateau beyond four workers. Together, our results offer a guide to spending an agent budget where it counts, given the task, cost, and latency constraints a user has.

While large language models (LLMs) have substantially improved Text-to-SQL generation, a pronounced gap remains between AI systems and human experts on challenging benchmarks such as BIRD-SQL. We argue this gap stems largely from the prevailing single-pass paradigm, which lacks the iterative reasoning, schema exploration, and error-correction behaviors that humans naturally employ. To address this limitation, we introduce SQL-Trail, a multi-turn reinforcement learning (RL) agentic framework for Text-to-SQL. Rather than producing a query in one shot, SQL-Trail interacts with the database environment and uses execution feedback to iteratively refine its predictions. Our approach centers on two key ideas: (i) an adaptive turn-budget allocation mechanism that scales the agent's interaction depth to match question difficulty, and (ii) a composite reward panel that jointly incentivizes SQL correctness and efficient exploration. Across benchmarks, SQL-Trail sets a new state of the art and delivers strong data efficiency--up to 18x higher than prior single-pass RL state-of-the-art methods. Notably, our 7B and 14B models outperform substantially larger proprietary systems by 5% on average, underscoring the effectiveness of interactive, agentic workflows for robust Text-to-SQL generation.

Learning control policies for complex, long-horizon tasks is a central challenge in robotics and autonomous systems. Signal Temporal Logic (STL) offers a powerful and expressive language for specifying such tasks, but its non-Markovian nature and inherent sparse reward make it difficult to be solved via standard Reinforcement Learning (RL) algorithms. Prior RL approaches focus only on limited STL fragments or use STL robustness scores as sparse terminal rewards. In this paper, we propose TGPO, Temporal Grounded Policy Optimization, to solve general STL tasks. TGPO decomposes STL into timed subgoals and invariant constraints and provides a hierarchical framework to tackle the problem. The high-level component of TGPO proposes concrete time allocations for these subgoals, and the low-level time-conditioned policy learns to achieve the sequenced subgoals using a dense, stage-wise reward signal. During inference, we sample various time allocations and select the most promising assignment for the policy network to rollout the solution trajectory. To foster efficient policy learning for complex STL with multiple subgoals, we leverage the learned critic to guide the high-level temporal search via Metropolis-Hastings sampling, focusing exploration on temporally feasible solutions. We conduct experiments on five environments, ranging from low-dimensional navigation to manipulation, drone, and quadrupedal locomotion. Under a wide range of STL tasks, TGPO significantly outperforms state-of-the-art baselines (especially for high-dimensional and long-horizon cases), with an average of 31.6% improvement in task success rate compared to the best baseline. The code will be available at https://github.com/mengyuest/TGPO

Recent breakthroughs in generative AI have transformed recommender systems through end-to-end generation. OneRec reformulates recommendation as an autoregressive generation task, achieving high Model FLOPs Utilization. While OneRec-V1 has shown significant empirical success in real-world deployment, two critical challenges hinder its scalability and performance: (1) inefficient computational allocation where 97.66% of resources are consumed by sequence encoding rather than generation, and (2) limitations in reinforcement learning relying solely on reward models. To address these challenges, we propose OneRec-V2, featuring: (1) Lazy Decoder-Only Architecture: Eliminates encoder bottlenecks, reducing total computation by 94% and training resources by 90%, enabling successful scaling to 8B parameters. (2) Preference Alignment with Real-World User Interactions: Incorporates Duration-Aware Reward Shaping and Adaptive Ratio Clipping to better align with user preferences using real-world feedback. Extensive A/B tests on Kuaishou demonstrate OneRec-V2's effectiveness, improving App Stay Time by 0.467%/0.741% while balancing multi-objective recommendations. This work advances generative recommendation scalability and alignment with real-world feedback, representing a step forward in the development of end-to-end recommender systems.

Through the collaboration of multiple LLM-empowered agents possessing diverse expertise and tools, multi-agent systems achieve impressive progress in solving real-world problems. Given the user queries, the meta-agents, serving as the brain within multi-agent systems, are required to decompose the queries into multiple sub-tasks that can be allocated to suitable agents capable of solving them, so-called agent-oriented planning. In this study, we identify three critical design principles of agent-oriented planning, including solvability, completeness, and non-redundancy, to ensure that each sub-task can be effectively resolved, resulting in satisfactory responses to user queries. These principles further inspire us to propose AOP, a novel framework for agent-oriented planning in multi-agent systems, leveraging a fast task decomposition and allocation process followed by an effective and efficient evaluation via a reward model. According to the evaluation results, the meta-agent is also responsible for promptly making necessary adjustments to sub-tasks and scheduling. Besides, we integrate a feedback loop into AOP to further enhance the effectiveness and robustness of such a problem-solving process. Extensive experiments demonstrate the advancement of AOP in solving real-world problems compared to both single-agent systems and existing planning strategies for multi-agent systems. The source code is available at https://github.com/lalaliat/Agent-Oriented-Planning

Multi-teacher on-policy distillation (M-OPD) has emerged as a promising paradigm for consolidating domain-specialized reinforcement learning (RL) experts into a single generalist student via dense, token-level reward supervision. Despite its practical success, the optimization dynamics governing multi-teacher capability integration remain poorly understood, and open, rigorously reproducible recipes are conspicuously lacking. In this work, we establish a controlled M-OPD benchmark on SmolLM3-3B-Base with oracle routing, isolating capability integration from routing ambiguity. Our investigation reveals a pronounced capability integration gap: standard M-OPD captures only 35.6% of the available headroom relative to a domain-routed oracle ensemble, with concise tasks such as instruction following suffering severe degradation and premature stagnation. Crucially, we show that this failure stems not from gradient conflict, but from a severe misallocation of the token-level optimization budget. This pathology is driven by three orthogonal factors: structural sequence-length disparities across domains, dynamic convergence drift due to non-uniform learning rates, and multi-step reward staleness from asynchronous policy updates. To resolve these imbalances, we introduce Open-MOPD, a principled framework incorporating token-share balancing, gap-aware dynamic budget allocation, and student reward refresh. Together, these mechanisms systematically restore cross-domain balance, elevating headroom recovery from 35.6% to 83.4% in a single deployable student. We fully open-source our end-to-end post-training recipe, training trajectories, and evaluation suites on an academically accessible hardware budget.

Autoformalization, translating natural-language mathematics into formal proof assistants, is bottlenecked not by translation fluency but by faithfulness: a formal statement can typecheck and be provable, yet still encode a different theorem than the source intended. We introduce Bidirectional Provability Fingerprinting (), a framework that certifies faithfulness by characterizing each candidate through its forward and backward consequence neighborhoods in the ambient theory and matching these against probes derived from the natural-language statement. We further introduce four novel components: (i) Counterfactual Probe Generation (), a contrastive procedure that synthesizes probes targeting specific drift directions; (ii) the Equivalence Spectrum, a continuous faithfulness score that replaces brittle binary verdicts; (iii) Adaptive Probe Budget Allocation (), an information-theoretic budget router; and (iv) Faithfulness-Guided Decoding (), which uses signals as a reward during autoformalization. We prove a drift detection theorem and a PAC-faithfulness result establishing that the equivalence class of a natural language statement is learnable from O(log(1/δ)/varepsilon) probes under mild assumptions. We release , a benchmark of 2{,}183 NL/Lean~4 pairs with controlled drift labels across six subfields of mathlib4. \,+\, detects 89.6% of drifted formalizations at a 3.0% false-positive rate-against 41.2% for typecheck and 63.3% for LLM-judge baselines, and reduces the rate at which a state-of-the-art autoformalizer emits drifted statements by 47%. https://pmlrbd.github.io/BPF/

Reinforcement learning from human feedback (RLHF) offers a promising approach to aligning large language models (LLMs) with human preferences. Typically, a reward model is trained or supplied to act as a proxy for humans in evaluating generated responses during the reinforcement training phase. However, current reward models operate as sequence-to-one models, allocating a single, sparse, and delayed reward to an entire output sequence. This approach may overlook the significant contributions of individual tokens toward the desired outcome. To this end, we propose a more fine-grained, token-level guidance approach for RL training. Specifically, we introduce RED, a novel reward redistribition method that evaluates and assigns specific credit to each token using an off-the-shelf reward model. Utilizing these fine-grained rewards enhances the model's understanding of language nuances, leading to more precise performance improvements. Notably, our method does not require modifying the reward model or introducing additional training steps, thereby incurring minimal computational costs. Experimental results across diverse datasets and tasks demonstrate the superiority of our approach.

Does high reward indicate productive coordination among language-model agents sharing resources? We examine this question in dining philosophers, where instances of the same model must acquire shared forks to eat. We evaluate seven model conditions across 630 episodes at five, ten, and fifteen philosophers, measuring scalar reward, deadlock, and meal throughput. At five philosophers, Mistral-Small 24B receives mean reward 0.827 while producing no meals. The reward decomposition explains this mismatch: avoiding deadlock earns a bonus without requiring meal production. To assess a policy trained with this reward, we compare the final checkpoint from a single Qwen3-14B group relative policy optimization (GRPO) training run with its base model. At five philosophers, the trained model has lower throughput (0.008 versus 0.020) and a higher deadlock rate in point estimates. Differences in mean episode reward are not statistically significant at any evaluated philosopher count. These findings show that the evaluated reward can assign high scores without task progress and support reporting behavioral measures alongside reward when comparing models and evaluating fine-tuned policies.

Credit assignment, the process of attributing credit or blame to individual agents for their contributions to a team's success or failure, remains a fundamental challenge in multi-agent reinforcement learning (MARL), particularly in environments with sparse rewards. Commonly-used approaches such as value decomposition often lead to suboptimal policies in these settings, and designing dense reward functions that align with human intuition can be complex and labor-intensive. In this work, we propose a novel framework where a large language model (LLM) generates dense, agent-specific rewards based on a natural language description of the task and the overall team goal. By learning a potential-based reward function over multiple queries, our method reduces the impact of ranking errors while allowing the LLM to evaluate each agent's contribution to the overall task. Through extensive experiments, we demonstrate that our approach achieves faster convergence and higher policy returns compared to state-of-the-art MARL baselines.

Reinforcement learning (RL) often encounters delayed and sparse feedback in real-world applications, even with only episodic rewards. Previous approaches have made some progress in reward redistribution for credit assignment but still face challenges, including training difficulties due to redundancy and ambiguous attributions stemming from overlooking the multifaceted nature of mission performance evaluation. Hopefully, Large Language Model (LLM) encompasses fruitful decision-making knowledge and provides a plausible tool for reward redistribution. Even so, deploying LLM in this case is non-trivial due to the misalignment between linguistic knowledge and the symbolic form requirement, together with inherent randomness and hallucinations in inference. To tackle these issues, we introduce LaRe, a novel LLM-empowered symbolic-based decision-making framework, to improve credit assignment. Key to LaRe is the concept of the Latent Reward, which works as a multi-dimensional performance evaluation, enabling more interpretable goal attainment from various perspectives and facilitating more effective reward redistribution. We examine that semantically generated code from LLM can bridge linguistic knowledge and symbolic latent rewards, as it is executable for symbolic objects. Meanwhile, we design latent reward self-verification to increase the stability and reliability of LLM inference. Theoretically, reward-irrelevant redundancy elimination in the latent reward benefits RL performance from more accurate reward estimation. Extensive experimental results witness that LaRe (i) achieves superior temporal credit assignment to SOTA methods, (ii) excels in allocating contributions among multiple agents, and (iii) outperforms policies trained with ground truth rewards for certain tasks.

Designing reward functions for efficiently guiding reinforcement learning (RL) agents toward specific behaviors is a complex task. This is challenging since it requires the identification of reward structures that are not sparse and that avoid inadvertently inducing undesirable behaviors. Naively modifying the reward structure to offer denser and more frequent feedback can lead to unintended outcomes and promote behaviors that are not aligned with the designer's intended goal. Although potential-based reward shaping is often suggested as a remedy, we systematically investigate settings where deploying it often significantly impairs performance. To address these issues, we introduce a new framework that uses a bi-level objective to learn behavior alignment reward functions. These functions integrate auxiliary rewards reflecting a designer's heuristics and domain knowledge with the environment's primary rewards. Our approach automatically determines the most effective way to blend these types of feedback, thereby enhancing robustness against heuristic reward misspecification. Remarkably, it can also adapt an agent's policy optimization process to mitigate suboptimalities resulting from limitations and biases inherent in the underlying RL algorithms. We evaluate our method's efficacy on a diverse set of tasks, from small-scale experiments to high-dimensional control challenges. We investigate heuristic auxiliary rewards of varying quality -- some of which are beneficial and others detrimental to the learning process. Our results show that our framework offers a robust and principled way to integrate designer-specified heuristics. It not only addresses key shortcomings of existing approaches but also consistently leads to high-performing solutions, even when given misaligned or poorly-specified auxiliary reward functions.

Reward design plays a pivotal role in aligning large language models (LLMs) with human values, serving as the bridge between feedback signals and model optimization. This survey provides a structured organization of reward modeling and addresses three key aspects: mathematical formulation, construction practices, and interaction with optimization paradigms. Building on this, it develops a macro-level taxonomy that characterizes reward mechanisms along complementary dimensions, thereby offering both conceptual clarity and practical guidance for alignment research. The progression of LLM alignment can be understood as a continuous refinement of reward design strategies, with recent developments highlighting paradigm shifts from reinforcement learning (RL)-based to RL-free optimization and from single-task to multi-objective and complex settings.

Current reinforcement learning from human feedback (RLHF) pipelines for large language model (LLM) alignment typically assign scalar rewards to sequences, using the final token as a surrogate indicator for the quality of the entire sequence. However, this leads to sparse feedback and suboptimal token-level credit assignment. In this work, we frame reward shaping as an optimization problem focused on token-level credit assignment. We propose a reward-shaping function leveraging explainability methods such as SHAP and LIME to estimate per-token rewards from the reward model. To learn parameters of this shaping function, we employ a bilevel optimization framework that integrates Bayesian Optimization and policy training to handle noise from the token reward estimates. Our experiments show that achieving a better balance of token-level reward attribution leads to performance improvements over baselines on downstream tasks and finds an optimal policy faster during training. Furthermore, we show theoretically that explainability methods that are feature additive attribution functions maintain the optimal policy as the original reward.

Reward engineering, the manual specification of reward functions to induce desired agent behavior, remains a fundamental challenge in multi-agent reinforcement learning. This difficulty is amplified by credit assignment ambiguity, environmental non-stationarity, and the combinatorial growth of interaction complexity. We argue that recent advances in large language models (LLMs) point toward a shift from hand-crafted numerical rewards to language-based objective specifications. Prior work has shown that LLMs can synthesize reward functions directly from natural language descriptions (e.g., EUREKA) and adapt reward formulations online with minimal human intervention (e.g., CARD). In parallel, the emerging paradigm of Reinforcement Learning from Verifiable Rewards (RLVR) provides empirical evidence that language-mediated supervision can serve as a viable alternative to traditional reward engineering. We conceptualize this transition along three dimensions: semantic reward specification, dynamic reward adaptation, and improved alignment with human intent, while noting open challenges related to computational overhead, robustness to hallucination, and scalability to large multi-agent systems. We conclude by outlining a research direction in which coordination arises from shared semantic representations rather than explicitly engineered numerical signals.

Recent advancements in reasoning language models have been driven by Reinforcement Learning (RL) fine-tuning. Most often, these rely on the Group Relative Policy Optimization (GRPO) algorithm or modifications thereof to steer the models to produce Chain-of-Thought (CoT) traces. The final answer can only be verified, and the reward assigned, after the CoT trace is complete, making it a delayed reward problem. GRPO and its modifications correspond to Monte Carlo methods in standard RL, which are known to suffer from high variance. A possible solution to this problem is the redistribution of rewards through credit assignment, where segments of the CoT trace that are important for arriving at the desirable solution are emphasized by assigning a higher reward. While Monte Carlo sampling can be used to provide an unbiased estimate of intermediate state values, its computational overhead makes it unsuitable for train-time credit assignment in long contexts at high granularity. We introduce RREDCoT (Reward REDistribution for Chain of Thoughts), which utilizes the model itself to approximate the optimal reward redistribution without additional generation. We investigate the advantages of our method compared to MC sampling and several attribution methods. We further analyze several aspects relevant to the construction of the redistribution such as segmentation of CoT traces and state value estimation.

Reward post-training of flow models either reweights the model's own samples under a KL penalty or a frozen reference, often for thousands of updates, or backpropagates the reward and moves every sample without checking that the move is worth its size. We introduce MEND, a reinforcement learning method built on proximal velocity matching. MEND caps rewards within each prompt group, so samples that already score well receive no move. Below the cap, it proposes moves along the reward gradient and accepts one only when its capped reward gain exceeds a quadratic displacement price. The model then regresses onto the resulting velocity targets, with no KL term, frozen reference model, or advantage weights. In 100 updates, MEND outperforms Flow-GRPO (about 4k updates) on five of six evaluators at the same distance to base-model images. Under an equal-budget protocol, it surpasses ReFL and DiffusionNFT at every evaluated update across four training rewards, reaching PickScore 24.03 versus 23.92 and 23.43, respectively. A 300-update three-reward run also surpasses the five-reward DiffusionNFT model on all three rewards it trains on. MEND is general and easy to adopt: it applies to any flow backbone with a differentiable reward.

Competitions for shareable and limited resources have long been studied with strategic agents. In reality, agents often have to learn and maximize the rewards of the resources at the same time. To design an individualized competing policy, we model the competition between agents in a novel multi-player multi-armed bandit (MPMAB) setting where players are selfish and aim to maximize their own rewards. In addition, when several players pull the same arm, we assume that these players averagely share the arms' rewards by expectation. Under this setting, we first analyze the Nash equilibrium when arms' rewards are known. Subsequently, we propose a novel SelfishMPMAB with Averaging Allocation (SMAA) approach based on the equilibrium. We theoretically demonstrate that SMAA could achieve a good regret guarantee for each player when all players follow the algorithm. Additionally, we establish that no single selfish player can significantly increase their rewards through deviation, nor can they detrimentally affect other players' rewards without incurring substantial losses for themselves. We finally validate the effectiveness of the method in extensive synthetic experiments.

Reward models play a key role in aligning language model applications towards human preferences. However, this setup creates an incentive for the language model to exploit errors in the reward model to achieve high estimated reward, a phenomenon often termed reward hacking. A natural mitigation is to train an ensemble of reward models, aggregating over model outputs to obtain a more robust reward estimate. We explore the application of reward ensembles to alignment at both training time (through reinforcement learning) and inference time (through reranking). First, we show that reward models are underspecified: reward models that perform similarly in-distribution can yield very different rewards when used in alignment, due to distribution shift. Second, underspecification results in overoptimization, where alignment to one reward model does not improve reward as measured by another reward model trained on the same data. Third, overoptimization is mitigated by the use of reward ensembles, and ensembles that vary by their pretraining seeds lead to better generalization than ensembles that differ only by their fine-tuning seeds, with both outperforming individual reward models. However, even pretrain reward ensembles do not eliminate reward hacking: we show several qualitative reward hacking phenomena that are not mitigated by ensembling because all reward models in the ensemble exhibit similar error patterns.

For multi-agent reinforcement learning systems (MARLS), the problem formulation generally involves investing massive reward engineering effort specific to a given problem. However, this effort often cannot be translated to other problems; worse, it gets wasted when system dynamics change drastically. This problem is further exacerbated in sparse reward scenarios, where a meaningful heuristic can assist in the policy convergence task. We propose GOVerned Reward Engineering Kernels (GOV-REK), which dynamically assign reward distributions to agents in MARLS during its learning stage. We also introduce governance kernels, which exploit the underlying structure in either state or joint action space for assigning meaningful agent reward distributions. During the agent learning stage, it iteratively explores different reward distribution configurations with a Hyperband-like algorithm to learn ideal agent reward models in a problem-agnostic manner. Our experiments demonstrate that our meaningful reward priors robustly jumpstart the learning process for effectively learning different MARL problems.

Reinforcement learning fine-tuning has become the dominant approach for aligning diffusion models with human preferences. However, assessing images is intrinsically a multi-dimensional task, and multiple evaluation criteria need to be optimized simultaneously. Existing practice deal with multiple rewards by training one specialist model per reward, optimizing a weighted-sum reward R(x)=sum_k w_k R_k(x), or sequentially fine-tuning with a hand-crafted stage schedule. These approaches either fail to produce a unified model that can be jointly trained on all rewards or necessitates heavy manually tuned sequential training. We find that the failure stems from using a naive weighted-sum reward aggregation. This approach suffers from a sample-level mismatch because most rollouts are specialist samples, highly informative for certain reward dimensions but irrelevant for others; consequently, weighted summation dilutes their supervision. To address this issue, we propose MARBLE (Multi-Aspect Reward BaLancE), a gradient-space optimization framework that maintains independent advantage estimators for each reward, computes per-reward policy gradients, and harmonizes them into a single update direction without manually-tuned reward weighting, by solving a Quadratic Programming problem. We further propose an amortized formulation that exploits the affine structure of the loss used in DiffusionNFT, to reduce the per-step cost from K+1 backward passes to near single-reward baseline cost, together with EMA smoothing on the balancing coefficients to stabilize updates against transient single-batch fluctuations. On SD3.5 Medium with five rewards, MARBLE improves all five reward dimensions simultaneously, turns the worst-aligned reward's gradient cosine from negative under weighted summation in 80% of mini-batches to consistently positive, and runs at 0.97X the training speed of baseline training.

In collaborative data sharing and machine learning, multiple parties aggregate their data resources to train a machine learning model with better model performance. However, as the parties incur data collection costs, they are only willing to do so when guaranteed incentives, such as fairness and individual rationality. Existing frameworks assume that all parties join the collaboration simultaneously, which does not hold in many real-world scenarios. Due to the long processing time for data cleaning, difficulty in overcoming legal barriers, or unawareness, the parties may join the collaboration at different times. In this work, we propose the following perspective: As a party who joins earlier incurs higher risk and encourages the contribution from other wait-and-see parties, that party should receive a reward of higher value for sharing data earlier. To this end, we propose a fair and time-aware data sharing framework, including novel time-aware incentives. We develop new methods for deciding reward values to satisfy these incentives. We further illustrate how to generate model rewards that realize the reward values and empirically demonstrate the properties of our methods on synthetic and real-world datasets.

In the last decade, Deep Reinforcement Learning has evolved into a powerful tool for complex sequential decision-making problems. It combines deep learning's proficiency in processing rich input signals with reinforcement learning's adaptability across diverse control tasks. At its core, an RL agent seeks to maximize its cumulative reward, enabling AI algorithms to uncover novel solutions previously unknown to experts. However, this focus on reward maximization also introduces a significant difficulty: improper reward specification can result in unexpected, misaligned agent behavior and inefficient learning. The complexity of accurately specifying the reward function is further amplified by the sequential nature of the task, the sparsity of learning signals, and the multifaceted aspects of the desired behavior. In this thesis, we survey the literature on effective reward specification strategies, identify core challenges relating to each of these approaches, and propose original contributions addressing the issue of sample efficiency and alignment in deep reinforcement learning. Reward specification represents one of the most challenging aspects of applying reinforcement learning in real-world domains. Our work underscores the absence of a universal solution to this complex and nuanced challenge; solving it requires selecting the most appropriate tools for the specific requirements of each unique application.

Reward models (RMs) provide critical feedback signals for LLM post-training, notably in reinforced fine-tuning (RFT) and reinforcement learning (RL) pipelines. However, current reward evaluation relies on heterogeneous criteria such as rule-based verifiers, ground-truth references, procedural checklists, and complex rubrics, where a unified mechanism to integrate all types of evidence remains unexplored. To this end, we propose Skill Reward Model (Skill-RM), a unified framework that reformulates reward modeling as the execution of a reusable Reward-Evaluation Skill. By treating reward computation as a structured agentic task, Skill-RM provides a consistent interface to orchestrate heterogeneous resources, dynamically selecting and aggregating evidence tailored to the specific requirements of each input. This approach enables the reward model to move beyond static evaluation, ensuring consistency and transparency across diverse tasks. Extensive experiments on reward benchmarks and downstream applications, including best-of-N selection and reinforcement learning, demonstrate that Skill-RM consistently outperforms traditional judge baselines. Our findings suggest that Skill-RM not only provides a unified solution for reward modeling but also achieves superior performance through the strategic and dynamic orchestration of evidence. The code is at https://github.com/Qwen-Applications/Skill-RM.

Reward sparsity in long-horizon reinforcement learning (RL) tasks remains a significant challenge, while existing outcome-based reward shaping struggles to define meaningful immediate rewards without introducing bias or requiring explicit task decomposition. Alternatively, verification-based reward shaping uses stepwise critics, but misalignment between immediate rewards and long-term objectives can lead to reward hacking and suboptimal policies. In this work, we address this problem in the context of software engineering (SWE) tasks, where multi-turn reasoning and rule-based verification are critical. We introduce the SWE-oriented RL Framework, a unified system supporting multi-turn interaction, docker-based execution, and customizable reward functions. Additionally, we propose Gated Reward Accumulation (G-RA), a novel method that accumulates immediate rewards only when high-level (long-term) rewards meet a predefined threshold, ensuring stable RL optimization. Experiments on SWE-bench Verified and kBench demonstrate that G-RA leads to an increase in completion rates (47.6\% \rightarrow 93.8\% and 22.0\% \rightarrow 86.0\%) and modification rates (19.6\% \rightarrow 23.8\% and 12.0\% \rightarrow 42.0\%), while avoiding policy degradation caused by reward misalignment. Our findings highlight the importance of balanced reward accumulation in long-horizon RL and provide a practical solution.

Reinforcement Learning (RL) has emerged as a mainstream paradigm for training Mobile GUI Agents, yet it struggles with the temporal credit assignment problem inherent in long-horizon tasks. A primary challenge lies in the trade-off between reward fidelity and density: outcome reward offers high fidelity but suffers from signal sparsity, while process reward provides dense supervision but remains prone to bias and reward hacking. To resolve this conflict, we propose the Adaptive Milestone Reward (ADMIRE) mechanism. ADMIRE constructs a verifiable, adaptive reward system by anchoring trajectory to milestones, which are dynamically distilled from successful explorations. Crucially, ADMIRE integrates an asymmetric credit assignment strategy that denoises successful trajectories and scaffolds failed trajectories. Extensive experiments demonstrate that ADMIRE consistently yields over 10% absolute improvement in success rate across different base models on AndroidWorld. Moreover, the method exhibits robust generalizability, achieving strong performance across diverse RL algorithms and heterogeneous environments such as web navigation and embodied tasks.

In order to solve a task using reinforcement learning, it is necessary to first formalise the goal of that task as a reward function. However, for many real-world tasks, it is very difficult to manually specify a reward function that never incentivises undesirable behaviour. As a result, it is increasingly popular to use reward learning algorithms, which attempt to learn a reward function from data. However, the theoretical foundations of reward learning are not yet well-developed. In particular, it is typically not known when a given reward learning algorithm with high probability will learn a reward function that is safe to optimise. This means that reward learning algorithms generally must be evaluated empirically, which is expensive, and that their failure modes are difficult to anticipate in advance. One of the roadblocks to deriving better theoretical guarantees is the lack of good methods for quantifying the difference between reward functions. In this paper we provide a solution to this problem, in the form of a class of pseudometrics on the space of all reward functions that we call STARC (STAndardised Reward Comparison) metrics. We show that STARC metrics induce both an upper and a lower bound on worst-case regret, which implies that our metrics are tight, and that any metric with the same properties must be bilipschitz equivalent to ours. Moreover, we also identify a number of issues with reward metrics proposed by earlier works. Finally, we evaluate our metrics empirically, to demonstrate their practical efficacy. STARC metrics can be used to make both theoretical and empirical analysis of reward learning algorithms both easier and more principled.

In collaborative learning with streaming data, nodes (e.g., organizations) jointly and continuously learn a machine learning (ML) model by sharing the latest model updates computed from their latest streaming data. For the more resourceful nodes to be willing to share their model updates, they need to be fairly incentivized. This paper explores an incentive design that guarantees fairness so that nodes receive rewards commensurate to their contributions. Our approach leverages an explore-then-exploit formulation to estimate the nodes' contributions (i.e., exploration) for realizing our theoretically guaranteed fair incentives (i.e., exploitation). However, we observe a "rich get richer" phenomenon arising from the existing approaches to guarantee fairness and it discourages the participation of the less resourceful nodes. To remedy this, we additionally preserve asymptotic equality, i.e., less resourceful nodes achieve equal performance eventually to the more resourceful/"rich" nodes. We empirically demonstrate in two settings with real-world streaming data: federated online incremental learning and federated reinforcement learning, that our proposed approach outperforms existing baselines in fairness and learning performance while remaining competitive in preserving equality.

Reward models are key in reinforcement learning from human feedback (RLHF) systems, aligning the model behavior with human preferences. Particularly in the math domain, there have been plenty of studies using reward models to align policies for improving reasoning capabilities. Recently, as the importance of reward models has been emphasized, RewardBench is proposed to understand their behavior. However, we figure out that the math subset of RewardBench has different representations between chosen and rejected completions, and relies on a single comparison, which may lead to unreliable results as it only see an isolated case. Therefore, it fails to accurately present the robustness of reward models, leading to a misunderstanding of its performance and potentially resulting in reward hacking. In this work, we introduce a new design for reliable evaluation of reward models, and to validate this, we construct RewardMATH, a benchmark that effectively represents the robustness of reward models in mathematical reasoning tasks. We demonstrate that the scores on RewardMATH strongly correlate with the results of optimized policy and effectively estimate reward overoptimization, whereas the existing benchmark shows almost no correlation. The results underscore the potential of our design to enhance the reliability of evaluation, and represent the robustness of reward model. We make our code and data publicly available.

In Reinforcement Learning (RL), an agent acts in an unknown environment to maximize the expected cumulative discounted sum of an external reward signal, i.e., the expected return. In practice, in many tasks of interest, such as policy optimization, the agent usually spends its interaction budget by collecting episodes of fixed length within a simulator (i.e., Monte Carlo simulation). However, given the discounted nature of the RL objective, this data collection strategy might not be the best option. Indeed, the rewards taken in early simulation steps weigh exponentially more than future rewards. Taking a cue from this intuition, in this paper, we design an a-priori budget allocation strategy that leads to the collection of trajectories of different lengths, i.e., truncated. The proposed approach provably minimizes the width of the confidence intervals around the empirical estimates of the expected return of a policy. After discussing the theoretical properties of our method, we make use of our trajectory truncation mechanism to extend Policy Optimization via Importance Sampling (POIS, Metelli et al., 2018) algorithm. Finally, we conduct a numerical comparison between our algorithm and POIS: the results are consistent with our theory and show that an appropriate truncation of the trajectories can succeed in improving performance.

Despite their widespread use, the role of reward models in shaping reinforcement learning is poorly understood. Reward models offer a tempting promise: they automatically estimate response quality in the absence of verifiers or human judges. Unlike "verifiable rewards" which typically produce binary scores, reward models typically produce continuous scores, allowing them to be sensitive to fine-grained differences in responses. However, we show this apparent strength is a serious weakness: many popular reward models are oversensitive, assigning different scores to equally good responses. Theoretically, we show that seemingly perfect reward models can be highly oversensitive; empirically, this oversensitivity can lead to bad policies. In place of existing notions of "reward model accuracy," we propose evaluating reward models using distinct measures of "discriminative ability" and "specificity" (the complement of oversensitivity). As a solution, we describe a training-free algorithm that uses Monte Carlo dropout on any neural reward model to produce discrete reward clusters. Theoretically, we prove there exist discretizations that reduce oversensitivity at minimal expense of discriminative ability; empirically we show, in both controlled and natural RL settings, that discretizing rewards leads to less reward hacking and better policies than training on the original rewards.

Large language models (LLMs) trained to answer questions are natively poor at teaching. Reinforcement Learning (RL) against a simulated student is a promising approach to improve their pedagogy, but existing RL-trained tutors reward the student's success on the tutored problem with the tutor's words still in context. The reward is then easiest to raise by telling the student the answer, and a tuned penalty is needed to reduce telling. Drawing on learning sciences, we introduce a masked near-transfer post-test: the student is tested on an unseen variant of the tutored problem with the tutor's utterances masked, so the reward can rise only through what the student wrote in its own turns. This discourages cognitive offloading by the student and allows the continuous penalty to be replaced by two binary reward gates (factual correctness of tutor response, no solution handover). A leave-one-out ablation shows that the learning-gain reward on its own does not separate teaching from telling: the gates reduce solution handover while the near-transfer post-test improves out-of-domain transfer. Using these reward designs we develop Eduardo, a multi-turn RL recipe for training LLM tutors, and use it to train 4B, 9B, 14B and 27B models from two distinct LLM architectures. Our post-trained Eduardo-27B model matches Gemini-3.1-Pro on MathTutorBench and Claude Opus 4.8 on TutorMoments at 2.4-6.2x fewer thinking tokens than frontier models, which matters for interactive tutoring. Without being named in the reward, the model more than doubles its use of the push-for-justification teacher move while support fading (e.g., assigning independent work), whose payoff lies beyond a single-problem dialog episode, is trained out. We open-source our training environment, an 8,671-problem near-transfer dataset, and trained models for further development.

The aim of Reinforcement Learning (RL) in real-world applications is to create systems capable of making autonomous decisions by learning from their environment through trial and error. This paper emphasizes the importance of reward engineering and reward shaping in enhancing the efficiency and effectiveness of reinforcement learning algorithms. Reward engineering involves designing reward functions that accurately reflect the desired outcomes, while reward shaping provides additional feedback to guide the learning process, accelerating convergence to optimal policies. Despite significant advancements in reinforcement learning, several limitations persist. One key challenge is the sparse and delayed nature of rewards in many real-world scenarios, which can hinder learning progress. Additionally, the complexity of accurately modeling real-world environments and the computational demands of reinforcement learning algorithms remain substantial obstacles. On the other hand, recent advancements in deep learning and neural networks have significantly improved the capability of reinforcement learning systems to handle high-dimensional state and action spaces, enabling their application to complex tasks such as robotics, autonomous driving, and game playing. This paper provides a comprehensive review of the current state of reinforcement learning, focusing on the methodologies and techniques used in reward engineering and reward shaping. It critically analyzes the limitations and recent advancements in the field, offering insights into future research directions and potential applications in various domains.

Automatically synthesizing dense rewards from natural language descriptions is a promising paradigm in reinforcement learning (RL), with applications to sparse reward problems, open-ended exploration, and hierarchical skill design. Recent works have made promising steps by exploiting the prior knowledge of large language models (LLMs). However, these approaches suffer from important limitations: they are either not scalable to problems requiring billions of environment samples, due to requiring LLM annotations for each observation, or they require a diverse offline dataset, which may not exist or be impossible to collect. In this work, we address these limitations through a combination of algorithmic and systems-level contributions. We propose \oni, a distributed architecture that simultaneously learns an RL policy and an intrinsic reward function using LLM feedback. Our approach annotates the agent's collected experience via an asynchronous LLM server, which is then distilled into an intrinsic reward model. We explore a range of algorithmic choices for reward modeling with varying complexity, including hashing, classification, and ranking models. By studying their relative tradeoffs, we shed light on questions regarding intrinsic reward design for sparse reward problems. Our approach achieves state-of-the-art performance across a range of challenging, sparse reward tasks from the NetHack Learning Environment in a simple unified process, solely using the agent's gathered experience, without requiring external datasets. We make our code available at https://github.com/facebookresearch/oni.

One of the challenges in applying reinforcement learning in a complex real-world environment lies in providing the agent with a sufficiently detailed reward function. Any misalignment between the reward and the desired behavior can result in unwanted outcomes. This may lead to issues like "reward hacking" where the agent maximizes rewards by unintended behavior. In this work, we propose to disentangle the reward into two distinct parts. A simple task-specific reward, outlining the particulars of the task at hand, and an unknown common-sense reward, indicating the expected behavior of the agent within the environment. We then explore how this common-sense reward can be learned from expert demonstrations. We first show that inverse reinforcement learning, even when it succeeds in training an agent, does not learn a useful reward function. That is, training a new agent with the learned reward does not impair the desired behaviors. We then demonstrate that this problem can be solved by training simultaneously on multiple tasks. That is, multi-task inverse reinforcement learning can be applied to learn a useful reward function.

Recent advances in aligning Large Language Models with human preferences have benefited from larger reward models and better preference data. However, most of these methodologies rely on the accuracy of the reward model. The reward models used in Reinforcement Learning with Human Feedback (RLHF) are typically learned from small datasets using stochastic optimization algorithms, making them prone to high variability. We illustrate the inconsistencies between reward models empirically on numerous open-source datasets. We theoretically show that the fluctuation of the reward models can be detrimental to the alignment problem because the derived policies are more overfitted to the reward model and, hence, are riskier if the reward model itself is uncertain. We use concentration of measure to motivate an uncertainty-aware, conservative algorithm for policy optimization. We show that such policies are more risk-averse in the sense that they are more cautious of uncertain rewards. We theoretically prove that our proposed methodology has less risk than the vanilla method. We corroborate our theoretical results with experiments based on designing an ensemble of reward models. We use this ensemble of reward models to align a language model using our methodology and observe that our empirical findings match our theoretical predictions.

Reward functions are central in reinforcement learning (RL), guiding agents towards optimal decision-making. The complexity of RL tasks requires meticulously designed reward functions that effectively drive learning while avoiding unintended consequences. Effective reward design aims to provide signals that accelerate the agent's convergence to optimal behavior. Crafting rewards that align with task objectives, foster desired behaviors, and prevent undesirable actions is inherently challenging. This thesis delves into the critical role of reward signals in RL, highlighting their impact on the agent's behavior and learning dynamics and addressing challenges such as delayed, ambiguous, or intricate rewards. In this thesis work, we tackle different aspects of reward shaping. First, we address the problem of designing informative and interpretable reward signals from a teacher's/expert's perspective (teacher-driven). Here, the expert, equipped with the optimal policy and the corresponding value function, designs reward signals that expedite the agent's convergence to optimal behavior. Second, we build on this teacher-driven approach by introducing a novel method for adaptive interpretable reward design. In this scenario, the expert tailors the rewards based on the learner's current policy, ensuring alignment and optimal progression. Third, we propose a meta-learning approach, enabling the agent to self-design its reward signals online without expert input (agent-driven). This self-driven method considers the agent's learning and exploration to establish a self-improving feedback loop.

Reinforcement Learning from Human Feedback (RLHF) is essential for aligning large language models (LLMs) with human values. However, RLHF is susceptible to reward hacking, where the agent exploits flaws in the reward function rather than learning the intended behavior, thus degrading alignment. While reward shaping helps stabilize RLHF and partially mitigate reward hacking, a systematic investigation into shaping techniques and their underlying principles remains lacking. To bridge this gap, we present a comprehensive study of the prevalent reward shaping methods. Our analysis suggests three key design principles: (1) RL reward is ideally bounded, (2) RL benefits from rapid initial growth followed by gradual convergence, and (3) RL reward is best formulated as a function of centered reward. Guided by these insights, we propose Preference As Reward (PAR), a novel approach that leverages the latent preferences embedded within the reward model itself as the signal for reinforcement learning. We evaluated PAR on two base models, Gemma2-2B and Llama3-8B, using two datasets, Ultrafeedback-Binarized and HH-RLHF. Experimental results demonstrate PAR's superior performance over other reward shaping methods. On the AlpacaEval 2.0 benchmark, PAR achieves a win rate at least 5 percentage points higher than competing approaches. Furthermore, PAR exhibits remarkable data efficiency, requiring only a single reference reward for optimal performance, and maintains robustness against reward hacking even after two full epochs of training. Code is available at https://github.com/PorUna-byte/PAR.

Large Language Models (LLMs) can self-improve through reinforcement learning, where they generate trajectories to explore and discover better solutions. However, this exploration process is computationally expensive, often forcing current methods to assign limited exploration budgets to each task. This uniform allocation creates problematic edge cases: easy tasks consistently succeed while difficult tasks consistently fail, both producing zero gradients during training updates for the widely used Group Relative Policy Optimization (GRPO). We address this problem from the lens of exploration budget allocation. Viewing each task's exploration as an "item" with a distinct "value" and "cost", we establish a connection to the classical knapsack problem. This formulation allows us to derive an optimal assignment rule that adaptively distributes resources based on the model's current learning status. When applied to GRPO, our method increases the effective ratio of non-zero policy gradients by 20-40% during training. Acting as a computational "free lunch", our approach could reallocate exploration budgets from tasks where learning is saturated to those where it is most impactful. This enables significantly larger budgets (e.g., 93 rollouts) for especially challenging problems, which would be computationally prohibitive under a uniform allocation. These improvements translate to meaningful gains on mathematical reasoning benchmarks, with average improvements of 2-4 points and peak gains of 9 points on specific tasks. Notably, achieving comparable performance with traditional homogeneous allocation would require about 2x the computational resources.

Reward models underpin the alignment of large language models, yet the dominant designs reduce each prompt--response pair to a point estimate or to a distribution from a fixed parametric family. This is at odds with human preference, which is inherently multimodal: the same response can be reasonably judged in many ways, and no single family covers all of them. To better fit this structure, we introduce DRM, a Diffusion Reward Model that recasts reward modeling as conditional density estimation over p(rmid x,y). Conditioned on a frozen LLM encoder, a lightweight Diffusion Transformer denoises Gaussian noise into a reward vector, placing no parametric assumption on the output distribution and naturally representing its multimodal structure. A single architecture handles both multi-attribute regression and pairwise preference data, and at inference N samples form an empirical reward distribution that can be aggregated into a scalar, a variance, or quantiles. Across five benchmarks, DRM matches or surpasses baselines under matched data and backbone, stays competitive with much larger discriminative, distributional, and generative RMs despite its modest training scale, and recovers multimodal reward structure where conventional heads collapse to a point. Uncertainty-aware rejection and lower-confidence-bound (LCB) aggregation further demonstrate that DRM can exploit distributional information beyond a scalar reward to improve reward-model decisions. Downstream RLHF experiments additionally show that using DRM as the training-time reward leads to improved policy performance, directly validating the practical benefit of diffusion-based reward modeling for RLHF training.

Reward models have been increasingly critical for improving the reasoning capability of LLMs. Existing research has shown that a well-trained reward model can substantially improve model performances at inference time via search. However, the potential of reward models during RL training time still remains largely under-explored. It is currently unclear whether these reward models can provide additional training signals to enhance the reasoning capabilities of LLMs in RL training that uses sparse success rewards, which verify the correctness of solutions. In this work, we evaluate popular reward models for RL training, including the Outcome-supervised Reward Model (ORM) and the Process-supervised Reward Model (PRM), and train a collection of LLMs for math problems using RL by combining these learned rewards with success rewards. Surprisingly, even though these learned reward models have strong inference-time performances, they may NOT help or even hurt RL training, producing worse performances than LLMs trained with the success reward only. Our analysis reveals that an LLM can receive high rewards from some of these reward models by repeating correct but unnecessary reasoning steps, leading to a severe reward hacking issue. Therefore, we introduce two novel reward refinement techniques, including Clipping and Delta. The key idea is to ensure the accumulative reward of any reasoning trajectory is upper-bounded to keep a learned reward model effective without being exploited. We evaluate our techniques with multiple reward models over a set of 1.5B and 7B LLMs on MATH and GSM8K benchmarks and demonstrate that with a carefully designed reward function, RL training without any additional supervised tuning can improve all the evaluated LLMs, including the state-of-the-art 7B LLM Qwen2.5-Math-7B-Instruct on MATH and GSM8K benchmarks.

Intrinsic rewards are designed to guide exploration in reinforcement learning by assigning value to an agent's experience, for example through prediction error or learning progress. However, maximizing these rewards need not produce the most informative experience available. We propose a formal criterion for exploration that compares policies by the counterfactual information they acquire: how well their histories can substitute for experience under alternative policies. We construct a single, simple environment in which specified count-based, prediction-error, empowerment, and information-gain objectives have maximizing policies that are Pareto-suboptimal at acquiring counterfactual information. We explain these failures and establish conditions under which existing intrinsic rewards successfully encourage optimal exploration. We also construct an objective that assigns a higher value whenever exploration strictly improves under our criterion.

Reinforcement learning is increasingly used for code-centric tasks. These tasks include code generation, summarization, understanding, repair, testing, and optimization. This trend is growing faster with large language models and autonomous agents. A key challenge is how to design reward signals that make sense for software. In many RL problems, the reward is a clear number. In software, this is often not possible. The goal is rarely a single numeric objective. Instead, rewards are usually proxies. Common proxies check if the code compiles, passes tests, or satisfies quality metrics. Many reward designs have been proposed for code-related tasks. However, the work is scattered across areas and papers. There is no single survey that brings these approaches together and shows the full landscape of reward design for RL in software. In this survey, we provide the first systematic and comprehensive review of reward engineering for RL in software tasks. We focus on existing methods and techniques. We structure the literature along three complementary dimensions, summarizing the reward-design choices within each. We conclude with challenges and recommendations in the reward design space for SE tasks.

Traditionally, reward models used for reinforcement learning from human feedback (RLHF) are trained to directly predict preference scores without leveraging the generation capabilities of the underlying large language model (LLM). This limits the capabilities of reward models as they must reason implicitly about the quality of a response, i.e., preference modeling must be performed in a single forward pass through the model. To enable reward models to reason explicitly about the quality of a response, we introduce Critique-out-Loud (CLoud) reward models. CLoud reward models operate by first generating a natural language critique of the assistant's response that is then used to predict a scalar reward for the quality of the response. We demonstrate the success of CLoud reward models for both Llama-3-8B and 70B base models: compared to classic reward models CLoud reward models improve pairwise preference classification accuracy on RewardBench by 4.65 and 5.84 percentage points for the 8B and 70B base models respectively. Furthermore, CLoud reward models lead to a Pareto improvement for win rate on ArenaHard when used as the scoring model for Best-of-N. Finally, we explore how to exploit the dynamic inference compute capabilities of CLoud reward models by performing self-consistency decoding for reward prediction.

Reward design in reinforcement learning (RL) is challenging since specifying human notions of desired behavior may be difficult via reward functions or require many expert demonstrations. Can we instead cheaply design rewards using a natural language interface? This paper explores how to simplify reward design by prompting a large language model (LLM) such as GPT-3 as a proxy reward function, where the user provides a textual prompt containing a few examples (few-shot) or a description (zero-shot) of the desired behavior. Our approach leverages this proxy reward function in an RL framework. Specifically, users specify a prompt once at the beginning of training. During training, the LLM evaluates an RL agent's behavior against the desired behavior described by the prompt and outputs a corresponding reward signal. The RL agent then uses this reward to update its behavior. We evaluate whether our approach can train agents aligned with user objectives in the Ultimatum Game, matrix games, and the DealOrNoDeal negotiation task. In all three tasks, we show that RL agents trained with our framework are well-aligned with the user's objectives and outperform RL agents trained with reward functions learned via supervised learning

We propose FlowRL: matching the full reward distribution via flow balancing instead of maximizing rewards in large language model (LLM) reinforcement learning (RL). Recent advanced reasoning models adopt reward-maximizing methods (\eg, PPO and GRPO), which tend to over-optimize dominant reward signals while neglecting less frequent but valid reasoning paths, thus reducing diversity. In contrast, we transform scalar rewards into a normalized target distribution using a learnable partition function, and then minimize the reverse KL divergence between the policy and the target distribution. We implement this idea as a flow-balanced optimization method that promotes diverse exploration and generalizable reasoning trajectories. We conduct experiments on math and code reasoning tasks: FlowRL achieves a significant average improvement of 10.0% over GRPO and 5.1% over PPO on math benchmarks, and performs consistently better on code reasoning tasks. These results highlight reward distribution-matching as a key step toward efficient exploration and diverse reasoning in LLM reinforcement learning.

To survive in dynamic and uncertain environments, individuals must develop effective decision strategies that balance information gathering and decision commitment. Models of such strategies often prioritize either optimizing tangible payoffs, like reward rate, or gathering information to support a diversity of (possibly unknown) objectives. However, our understanding of the relative merits of these two approaches remains incomplete, in part because direct comparisons have been limited to idealized, static environments that lack the dynamic complexity of the real world. Here we compared the performance of normative reward- and information-seeking strategies in a dynamic foraging task. Both strategies show similar transitions between exploratory and exploitative behaviors as environmental uncertainty changes. However, we find subtle disparities in the actions they take, resulting in meaningful performance differences: whereas reward-seeking strategies generate slightly more reward on average, information-seeking strategies provide more consistent and predictable outcomes. Our findings support the adaptive value of information-seeking behaviors that can mitigate risk with minimal reward loss.

Reinforcement Learning from Human Feedback (RLHF) is a pivotal technique for aligning large language models (LLMs) with human preferences, yet it is susceptible to reward overoptimization, in which policy models overfit to the reward model, exploit spurious reward patterns instead of faithfully capturing human intent. Prior mitigations primarily relies on surface semantic information and fails to efficiently address the misalignment between the reward model (RM) and the policy model caused by continuous policy distribution shifts. This inevitably leads to an increasing reward discrepancy, exacerbating reward overoptimization. To address these limitations, we introduce R2M (Real-Time Aligned Reward Model), a novel lightweight RLHF framework. R2M goes beyond vanilla reward models that solely depend on the semantic representations of a pretrained LLM. Instead, it leverages the evolving hidden states of the policy (namely policy feedback) to align with the real-time distribution shift of the policy during the RL process. This work points to a promising new direction for improving the performance of reward models through real-time utilization of feedback from policy models.

Text-to-image generation enables users to explore several images generated from the same prompt. For these generated images to be useful, each one must reflect the user's preferences, measured by a learned reward, and differ visually from the others to maintain diversity. Existing methods are limited: they either address reward and diversity separately or combine them in one aggregate score, enabling high diversity to offset low rewards. In this paper, we address these limitations by formulating generation as satisficing: every image (candidate) must satisfy a reward floor and the batch of images must satisfy a diversity cutoff. The reward floor controls the balance between worst-candidate reward and batch diversity; we show that varying this floor defines a Pareto frontier. To traverse this frontier, we introduce SatisDive, a training-free inference-time method. SatisDive uses a batch-relative reward cutoff to distinguish lower- from higher-reward candidates, emphasizing reward improvement for candidates below the cutoff and diversity among candidates above it. On Pick-a-Pic, at matched DreamSim, SatisDive improves worst-candidate reward over FK steering by up to 0.43 with FLUX.1-dev as the base model and HPSv3 as the reward, and by up to 0.70 with SANA-1.6B as the base model and ImageReward as the reward. More broadly, across their overlapping DreamSim ranges, SatisDive's satisfaction-diversity curve Pareto-dominates FK steering's curve in each setting.

We aim to improve model performance in multi-reward reinforcement learning training process. Existing Group reward-Decoupled Normalization Policy Optimization (GDPO) has mitigated the issue of reward signals masking one another during direct scalarization by normalizing each reward dimension separately before aggregation. However, our experiments show that GDPO still struggles to balance reward signals with different granularities. Specifically, in some particular training tasks, the model may receive a dense reward that assigns fine-grained scores ranging from 0.1 to 1.0, together with a sparse reward that provides only binary feedback of either 0 or 1. In such cases, we find that the sparse reward may provide an insufficient optimization signal, preventing its corresponding capability from being effectively reinforced. Therefore, how can we strengthen the optimization signal from the sparse reward without sacrificing the capability already learned from the fine-grained reward? To overcome this limitation, we propose Specialize-and-Merge Online Policy Distillation (SMOPD), a two-stage training method for multi-reward optimization. Stage1-Specialize: SMOPD first employs reward-priority configurations to train multiple reward-specialized teachers, allowing each reward to be learned under conditions where its signal can effectively drive optimization. Stage2-Merge: SMOPD then utilizes online policy distillation to combine the reward-specialized capabilities of these teachers into a single student policy, while maintaining balanced task-level optimization. To validate our method, we conduct experiments on two multi-reward settings: complementary rewards(tool-calling accuracy and format) and conflicting rewards (helpful and harmless rewards). Based on above settings, SMOPD outperforms GDPO across 1.5B, 3B and 7B backbones.

Reinforcement learning usually uses the feedback rewards of environmental to train agents. But the rewards in the actual environment are sparse, and even some environments will not rewards. Most of the current methods are difficult to get good performance in sparse reward or non-reward environments. Although using shaped rewards is effective when solving sparse reward tasks, it is limited to specific problems and learning is also susceptible to local optima. We propose a model-free method that does not rely on environmental rewards to solve the problem of sparse rewards in the general environment. Our method use the minimum number of transitions between states as the distance to replace the rewards of environmental, and proposes a goal-distance gradient to achieve policy improvement. We also introduce a bridge point planning method based on the characteristics of our method to improve exploration efficiency, thereby solving more complex tasks. Experiments show that our method performs better on sparse reward and local optimal problems in complex environments than previous work.

In this paper we argue for the fundamental importance of the value distribution: the distribution of the random return received by a reinforcement learning agent. This is in contrast to the common approach to reinforcement learning which models the expectation of this return, or value. Although there is an established body of literature studying the value distribution, thus far it has always been used for a specific purpose such as implementing risk-aware behaviour. We begin with theoretical results in both the policy evaluation and control settings, exposing a significant distributional instability in the latter. We then use the distributional perspective to design a new algorithm which applies Bellman's equation to the learning of approximate value distributions. We evaluate our algorithm using the suite of games from the Arcade Learning Environment. We obtain both state-of-the-art results and anecdotal evidence demonstrating the importance of the value distribution in approximate reinforcement learning. Finally, we combine theoretical and empirical evidence to highlight the ways in which the value distribution impacts learning in the approximate setting.

Reward hacking--where agents exploit flaws in imperfect reward functions rather than performing tasks as intended--poses risks for AI alignment. Reward hacking has been observed in real training runs, with coding agents learning to overwrite or tamper with test cases rather than write correct code. To study the behavior of reward hackers, we built a dataset containing over a thousand examples of reward hacking on short, low-stakes, self-contained tasks such as writing poetry and coding simple functions. We used supervised fine-tuning to train models (GPT-4.1, GPT-4.1-mini, Qwen3-32B, Qwen3-8B) to reward hack on these tasks. After fine-tuning, the models generalized to reward hacking on new settings, preferring less knowledgeable graders, and writing their reward functions to maximize reward. Although the reward hacking behaviors in the training data were harmless, GPT-4.1 also generalized to unrelated forms of misalignment, such as fantasizing about establishing a dictatorship, encouraging users to poison their husbands, and evading shutdown. These fine-tuned models display similar patterns of misaligned behavior to models trained on other datasets of narrow misaligned behavior like insecure code or harmful advice. Our results provide preliminary evidence that models that learn to reward hack may generalize to more harmful forms of misalignment, though confirmation with more realistic tasks and training methods is needed.

Preference based Reinforcement Learning (PbRL) removes the need to hand specify a reward function by learning a reward from preference feedback over policy behaviors. Current approaches to PbRL do not address the credit assignment problem inherent in determining which parts of a behavior most contributed to a preference, which result in data intensive approaches and subpar reward functions. We address such limitations by introducing a credit assignment strategy (Hindsight PRIOR) that uses a world model to approximate state importance within a trajectory and then guides rewards to be proportional to state importance through an auxiliary predicted return redistribution objective. Incorporating state importance into reward learning improves the speed of policy learning, overall policy performance, and reward recovery on both locomotion and manipulation tasks. For example, Hindsight PRIOR recovers on average significantly (p<0.05) more reward on MetaWorld (20%) and DMC (15%). The performance gains and our ablations demonstrate the benefits even a simple credit assignment strategy can have on reward learning and that state importance in forward dynamics prediction is a strong proxy for a state's contribution to a preference decision. Code repository can be found at https://github.com/apple/ml-rlhf-hindsight-prior.

Large pretrained models are showing increasingly better performance in reasoning and planning tasks across different modalities, opening the possibility to leverage them for complex sequential decision making problems. In this paper, we investigate the capabilities of Large Language Models (LLMs) for reinforcement learning (RL) across a diversity of interactive domains. We evaluate their ability to produce decision-making policies, either directly, by generating actions, or indirectly, by first generating reward models to train an agent with RL. Our results show that, even without task-specific fine-tuning, LLMs excel at reward modeling. In particular, crafting rewards through artificial intelligence (AI) feedback yields the most generally applicable approach and can enhance performance by improving credit assignment and exploration. Finally, in environments with unfamiliar dynamics, we explore how fine-tuning LLMs with synthetic data can significantly improve their reward modeling capabilities while mitigating catastrophic forgetting, further broadening their utility in sequential decision-making tasks.

Task allocation is a key combinatorial optimization problem, crucial for modern applications such as multi-robot cooperation and resource scheduling. Decision makers must allocate entities to tasks reasonably across different scenarios. However, traditional methods assume static attributes and numbers of tasks and entities, often relying on dynamic programming and heuristic algorithms for solutions. In reality, task allocation resembles Markov decision processes, with dynamically changing task and entity attributes. Thus, algorithms must dynamically allocate tasks based on their states. To address this issue, we propose a two-stage task allocation algorithm based on similarity, utilizing reinforcement learning to learn allocation strategies. The proposed pre-assign strategy allows entities to preselect appropriate tasks, effectively avoiding local optima and thereby better finding the optimal allocation. We also introduce an attention mechanism and a hyperparameter network structure to adapt to the changing number and attributes of entities and tasks, enabling our network structure to generalize to new tasks. Experimental results across multiple environments demonstrate that our algorithm effectively addresses the challenges of dynamic task allocation in practical applications. Compared to heuristic algorithms like genetic algorithms, our reinforcement learning approach better solves dynamic allocation problems and achieves zero-shot generalization to new tasks with good performance. The code is available at https://github.com/yk7333/TaskAllocation.

When audio, video, and text disagree, accuracy alone does not show whether to acquire another source or abstain. We study these choices in a controlled three-score benchmark: a policy observes two signed scores, may request the third at a cost, and can abstain. The primary reward is mechanism-specific: abstention is correct only for one designated ambiguity mechanism and is penalized under mixed corruption. Matched controls show that a threshold policy matches always-request decisions with fewer requests; its advantage over always-answer fusion depends on the reward assigned to that ambiguity. On a partially held-out synthetic split, the threshold policy reaches 0.789 +/- 0.006 targeted decision accuracy and 0.481 +/- 0.014 utility across 83 seeds. A three-score majority reference reaches 0.626 +/- 0.008 and 0.252 +/- 0.016, but uses more information. In a matched-budget test, a train-only value selector improves utility over no-query and matched-random policies at 10% and 25% budgets, while pair uncertainty has higher utility at every budget. At 50% and 63.7% budgets, the selector lowers utility despite slightly higher non-ambiguous accuracy. If all abstentions are scored incorrect, majority outranks the threshold policy in utility. At a central temporal setting, full-trace controls match the neural models while position perturbations separate them. On held-out-actor emotion clips, eight-frame fusion has opposite-signed accuracy differences for two encoder pairs, with both actor intervals containing zero; matched-request routing gains are small and uncertain. These results separate full-modality accuracy from pre-request selection value and show that selection value depends on budget and the observed-pair ranking.

Reinforcement learning from human feedback (RLHF) is bottlenecked by reward hacking, where the policy exploits errors in a proxy reward model (RM) and produces high RM scores without genuine quality gains. A natural mitigation is pessimism: lowering rewards in regions where the RM is uncertain. However, standard scalar RMs provide no principled notion of uncertainty. We argue that the right object is a distributional reward model p(rmid x,y). Under either a Bayesian inference or a KL-distributionally robust optimization (KL-DRO) lens, the KL-regularized RLHF objective admits a closed-form effective reward tilde r(x,y) = pmβlogE_p[e^{pm r/β}]. The pessimistic branch unifies the prior heuristics for RM ensemble aggregation: mean aggregation, worst-case optimization (WCO), and uncertainty-weighted optimization (UWO) all emerge as limits or truncations of this single expression. This also clarifies the implicit assumptions of each existing rule.

Reward modeling (RM), which captures human preferences to align large language models (LLMs), is increasingly employed in tasks such as model finetuning, response filtering, and ranking. However, due to the inherent complexity of human preferences and the limited coverage of available datasets, reward models often fail under distributional shifts or adversarial perturbations. Existing approaches for identifying such failure modes typically rely on prior knowledge about preference distributions or failure attributes, limiting their practicality in real-world settings where such information is unavailable. In this work, we propose a tractable, preference-distribution agnostic method for discovering reward model failure modes via reward guided controlled decoding. Building on this, we introduce REFORM, a self-improving reward modeling framework that enhances robustness by using the reward model itself to guide the generation of falsely scored responses. These adversarial examples are then used to augment the training data and patch the reward model's misaligned behavior. We evaluate REFORM on two widely used preference datasets Anthropic Helpful Harmless (HH) and PKU Beavertails and demonstrate that it significantly improves robustness without sacrificing reward quality. Notably, REFORM preserves performance both in direct evaluation and in downstream policy training, and further improves alignment quality by removing spurious correlations.

Reinforcement Learning from Human Feedback has emerged as a standard for aligning diffusion models. However, we identify a fundamental limitation in the standard DPO formulation because it relies on the Bradley-Terry model to aggregate diverse evaluation axes like aesthetic quality and semantic alignment into a single scalar reward. This aggregation creates a reward conflict where the model is forced to unlearn desirable features of a specific dimension if they appear in a globally non-preferred sample. To address this issue, we propose Multi Reward Conditional DPO (MCDPO). This method resolves reward conflicts by introducing a disentangled Bradley-Terry objective. MCDPO explicitly injects a preference outcome vector as a condition during training, which allows the model to learn the correct optimization direction for each reward axis independently within a single network. We further introduce dimensional reward dropout to ensure balanced optimization across dimensions. Extensive experiments on Stable Diffusion 1.5 and SDXL demonstrate that MCDPO achieves superior performance on benchmarks. Notably, our conditional framework enables dynamic and multiple-axis control at inference time using Classifier Free Guidance to amplify specific reward dimensions without additional training or external reward models.

Large language models (LLMs) have demonstrated remarkable performance in reasoning tasks, where reinforcement learning (RL) serves as a key algorithm for enhancing their reasoning capabilities. Currently, there are two mainstream reward paradigms: model-based rewards and rule-based rewards. However, both approaches suffer from limitations: rule-based rewards lack robustness, while model-based rewards are vulnerable to reward hacking. To address these issues, we propose Cooper(Co-optimizing Policy Model and Reward Model), a RL framework that jointly optimizes both the policy model and the reward model. Cooper leverages the high precision of rule-based rewards when identifying correct responses, and dynamically constructs and selects positive-negative sample pairs for continued training the reward model. This design enhances robustness and mitigates the risk of reward hacking. To further support Cooper, we introduce a hybrid annotation strategy that efficiently and accurately generates training data for the reward model. We also propose a reference-based reward modeling paradigm, where the reward model takes a reference answer as input. Based on this design, we train a reward model named VerifyRM, which achieves higher accuracy on VerifyBench compared to other models of the same size. We conduct reinforcement learning using both VerifyRM and Cooper. Our experiments show that Cooper not only alleviates reward hacking but also improves end-to-end RL performance, for instance, achieving a 0.54% gain in average accuracy on Qwen2.5-1.5B-Instruct. Our findings demonstrate that dynamically updating reward model is an effective way to combat reward hacking, providing a reference for better integrating reward models into RL.

Reinforcement Learning from Human Feedback (RLHF) has been crucial to the recent success of Large Language Models (LLMs), however, it is often a complex and brittle process. In the classical RLHF framework, a reward model is first trained to represent human preferences, which is in turn used by an online reinforcement learning (RL) algorithm to optimize the LLM. A prominent issue with such methods is reward over-optimization or reward hacking, where performance as measured by the learned proxy reward model increases, but true quality plateaus or even deteriorates. Direct Alignment Algorithms (DDAs) like Direct Preference Optimization have emerged as alternatives to the classical RLHF pipeline by circumventing the reward modeling phase. However, although DAAs do not use a separate proxy reward model, they still commonly deteriorate from over-optimization. While the so-called reward hacking phenomenon is not well-defined for DAAs, we still uncover similar trends: at higher KL budgets, DAA algorithms exhibit similar degradation patterns to their classic RLHF counterparts. In particular, we find that DAA methods deteriorate not only across a wide range of KL budgets but also often before even a single epoch of the dataset is completed. Through extensive empirical experimentation, this work formulates and formalizes the reward over-optimization or hacking problem for DAAs and explores its consequences across objectives, training regimes, and model scales.

Reinforcement Learning from Human Feedback (RLHF) has become a crucial technology for aligning language models with human values and intentions, enabling models to produce more helpful and harmless responses. Reward models are trained as proxies for human preferences to drive reinforcement learning optimization. While reward models are often considered central to achieving high performance, they face the following challenges in practical applications: (1) Incorrect and ambiguous preference pairs in the dataset may hinder the reward model from accurately capturing human intent. (2) Reward models trained on data from a specific distribution often struggle to generalize to examples outside that distribution and are not suitable for iterative RLHF training. In this report, we attempt to address these two issues. (1) From a data perspective, we propose a method to measure the strength of preferences within the data, based on a voting mechanism of multiple reward models. Experimental results confirm that data with varying preference strengths have different impacts on reward model performance. We introduce a series of novel methods to mitigate the influence of incorrect and ambiguous preferences in the dataset and fully leverage high-quality preference data. (2) From an algorithmic standpoint, we introduce contrastive learning to enhance the ability of reward models to distinguish between chosen and rejected responses, thereby improving model generalization. Furthermore, we employ meta-learning to enable the reward model to maintain the ability to differentiate subtle differences in out-of-distribution samples, and this approach can be utilized for iterative RLHF optimization.

Extrinsic rewards can effectively guide reinforcement learning (RL) agents in specific tasks. However, extrinsic rewards frequently fall short in complex environments due to the significant human effort needed for their design and annotation. This limitation underscores the necessity for intrinsic rewards, which offer auxiliary and dense signals and can enable agents to learn in an unsupervised manner. Although various intrinsic reward formulations have been proposed, their implementation and optimization details are insufficiently explored and lack standardization, thereby hindering research progress. To address this gap, we introduce RLeXplore, a unified, highly modularized, and plug-and-play framework offering reliable implementations of eight state-of-the-art intrinsic reward methods. Furthermore, we conduct an in-depth study that identifies critical implementation details and establishes well-justified standard practices in intrinsically-motivated RL. Our documentation, examples, and source code are available at https://github.com/RLE-Foundation/RLeXplore.

Fine-tuning large language models (LLMs) on reasoning benchmarks via reinforcement learning requires a specific reward function, often binary, for each benchmark. This comes with two potential limitations: the need to design the reward, and the potentially sparse nature of binary rewards. Here, we systematically investigate rewards derived from the probability or log-probability of emitting the reference answer (or any other prompt continuation present in the data), which have the advantage of not relying on specific verifiers and being available at scale. Several recent works have advocated for the use of similar rewards (e.g., VeriFree, JEPO, RLPR, NOVER). We systematically compare variants of likelihood-based rewards with standard baselines, testing performance both on standard mathematical reasoning benchmarks, and on long-form answers where no external verifier is available. We find that using the log-probability of the reference answer as the reward for chain-of-thought (CoT) learning is the only option that performs well in all setups. This reward is also consistent with the next-token log-likelihood loss used during pretraining. In verifiable settings, log-probability rewards bring comparable or better success rates than reinforcing with standard binary rewards, and yield much better perplexity. In non-verifiable settings, they perform on par with SFT. On the other hand, methods based on probability, such as VeriFree, flatline on non-verifiable settings due to vanishing probabilities of getting the correct answer. Overall, this establishes log-probability rewards as a viable method for CoT fine-tuning, bridging the short, verifiable and long, non-verifiable answer settings.

The temporal credit assignment problem is a central challenge in Reinforcement Learning (RL), concerned with attributing the appropriate influence to each actions in a trajectory for their ability to achieve a goal. However, when feedback is delayed and sparse, the learning signal is poor, and action evaluation becomes harder. Canonical solutions, such as reward shaping and options, require extensive domain knowledge and manual intervention, limiting their scalability and applicability. In this work, we lay the foundations for Credit Assignment with Language Models (CALM), a novel approach that leverages Large Language Models (LLMs) to automate credit assignment via reward shaping and options discovery. CALM uses LLMs to decompose a task into elementary subgoals and assess the achievement of these subgoals in state-action transitions. Every time an option terminates, a subgoal is achieved, and CALM provides an auxiliary reward. This additional reward signal can enhance the learning process when the task reward is sparse and delayed without the need for human-designed rewards. We provide a preliminary evaluation of CALM using a dataset of human-annotated demonstrations from MiniHack, suggesting that LLMs can be effective in assigning credit in zero-shot settings, without examples or LLM fine-tuning. Our preliminary results indicate that the knowledge of LLMs is a promising prior for credit assignment in RL, facilitating the transfer of human knowledge into value functions.

Standard reinforcement learning from human feedback (RLHF) trains a reward model on pairwise preference data and then uses it for policy optimization. However, while reward models are optimized to capture relative preferences, existing policy optimization techniques rely on absolute reward magnitudes during training. In settings where the rewards are non-verifiable such as summarization, instruction following, and chat completion, this misalignment often leads to suboptimal performance. We introduce Group Ordinal Policy Optimization (GOPO), a policy optimization method that uses only the ranking of the rewards and discards their magnitudes. Our rank-based transformation of rewards provides several gains, compared to Group Relative Policy Optimization (GRPO), in settings with non-verifiable rewards: (1) consistently higher training/validation reward trajectories, (2) improved LLM-as-judge evaluations across most intermediate training steps, and (3) reaching a policy of comparable quality in substantially less training steps than GRPO. We demonstrate consistent improvements across a range of tasks and model sizes.

We propose a new complexity measure for Markov decision processes (MDPs), the maximum expected hitting cost (MEHC). This measure tightens the closely related notion of diameter [JOA10] by accounting for the reward structure. We show that this parameter replaces diameter in the upper bound on the optimal value span of an extended MDP, thus refining the associated upper bounds on the regret of several UCRL2-like algorithms. Furthermore, we show that potential-based reward shaping [NHR99] can induce equivalent reward functions with varying informativeness, as measured by MEHC. We further establish that shaping can reduce or increase MEHC by at most a factor of two in a large class of MDPs with finite MEHC and unsaturated optimal average rewards.

Language models trained with reinforcement learning may learn to optimize the grader's judgment rather than the intended objective. This "reward-seeking" is difficult to measure because a model that pursues the grader's judgment and one that pursues the intended objective behave identically whenever the grader rewards the intended behavior. We measure reward-seeking using Contrastive Synthetic Document Finetuning to change a model's beliefs about what the grader rewards, putting those beliefs in conflict with what users or developers want, and measuring the rate at which the model adopts each party's preferred behavior. Applied to intermediate checkpoints of a capabilities-focused OpenAI o3 RL run, without safety training, we find that these checkpoints often side with grader preferences over those of users or developers on coding and alignment tasks. This tendency to side with the grader trends upward throughout RL training. For example, in an environment that forces a choice between keeping a promise to a supervisor and breaking it to complete the task, a late capabilities-focused o3 checkpoint breaks the promise 87% of the time when SDF documents say the grader rewards task completion, versus 9% when they say it rewards honesty (a choice its chain-of-thought often makes explicit). An earlier checkpoint is far less sensitive (40% vs. 24%). Our method also generalizes to reward-hacking models. A model organism trained to reward-hack (gpt-oss-120b) is more than twice as sensitive to grader preferences as the unmodified model, with the mean behavioral shift in favor of the grader rising from 33% to 86%. These results indicate that RL can increase reward-seeking over the course of training, producing models that may act against their developers' intentions when they believe that doing so leads to higher reward.

A growing trend for value-based reinforcement learning (RL) algorithms is to capture more information than scalar value functions in the value network. One of the most well-known methods in this branch is distributional RL, which models return distribution instead of scalar value. In another line of work, hybrid reward architectures (HRA) in RL have studied to model source-specific value functions for each source of reward, which is also shown to be beneficial in performance. To fully inherit the benefits of distributional RL and hybrid reward architectures, we introduce Multi-Dimensional Distributional DQN (MD3QN), which extends distributional RL to model the joint return distribution from multiple reward sources. As a by-product of joint distribution modeling, MD3QN can capture not only the randomness in returns for each source of reward, but also the rich reward correlation between the randomness of different sources. We prove the convergence for the joint distributional Bellman operator and build our empirical algorithm by minimizing the Maximum Mean Discrepancy between joint return distribution and its Bellman target. In experiments, our method accurately models the joint return distribution in environments with richly correlated reward functions, and outperforms previous RL methods utilizing multi-dimensional reward functions in the control setting.

Recent reinforcement learning (RL) approaches have shown strong performance in complex domains such as Atari games, but are often highly sample inefficient. A common approach to reduce interaction time with the environment is to use reward shaping, which involves carefully designing reward functions that provide the agent intermediate rewards for progress towards the goal. However, designing appropriate shaping rewards is known to be difficult as well as time-consuming. In this work, we address this problem by using natural language instructions to perform reward shaping. We propose the LanguagE-Action Reward Network (LEARN), a framework that maps free-form natural language instructions to intermediate rewards based on actions taken by the agent. These intermediate language-based rewards can seamlessly be integrated into any standard reinforcement learning algorithm. We experiment with Montezuma's Revenge from the Atari Learning Environment, a popular benchmark in RL. Our experiments on a diverse set of 15 tasks demonstrate that, for the same number of interactions with the environment, language-based rewards lead to successful completion of the task 60% more often on average, compared to learning without language.

Reward models (RMs) are at the crux of successful RLHF to align pretrained models to human preferences, yet there has been relatively little study that focuses on evaluation of those reward models. Evaluating reward models presents an opportunity to understand the opaque technologies used for alignment of language models and which values are embedded in them. To date, very few descriptors of capabilities, training methods, or open-source reward models exist. In this paper, we present RewardBench, a benchmark dataset and code-base for evaluation, to enhance scientific understanding of reward models. The RewardBench dataset is a collection of prompt-win-lose trios spanning chat, reasoning, and safety, to benchmark how reward models perform on challenging, structured and out-of-distribution queries. We created specific comparison datasets for RMs that have subtle, but verifiable reasons (e.g. bugs, incorrect facts) why one answer should be preferred to another. On the RewardBench leaderboard, we evaluate reward models trained with a variety of methods, such as the direct MLE training of classifiers and the implicit reward modeling of Direct Preference Optimization (DPO), and on a spectrum of datasets. We present many findings on propensity for refusals, reasoning limitations, and instruction following shortcomings of various reward models towards a better understanding of the RLHF process.

Reinforcement learning (RL) can align language models with non-differentiable reward signals, such as human preferences. However, a major challenge arises from the sparsity of these reward signals - typically, there is only one reward for the entire generation. This sparsity of rewards can lead to inefficient and unstable learning. In this paper, we introduce a novel framework leveraging the critique ability of LLMs to produce dense rewards throughout the learning process. Our approach incorporates a critic language model alongside the policy model. This critic is prompted with the task description, question, policy model's output, and environment's reward signal as input, and provides token or span-level dense rewards that reflect the quality of each segment of the output. We assess our approach on three text generation tasks: sentiment control, language model detoxification, and summarization. Experimental results show that incorporating artificial dense rewards in training yields consistent performance gains over the PPO baseline with holistic rewards. Furthermore, in a setting where the same model serves as both policy and critic, we demonstrate that "self-critique" rewards also boost learning efficiency.

In reinforcement learning (RL), an agent learns to perform a task by interacting with an environment and receiving feedback (a numerical reward) for its actions. However, the assumption that rewards are always observable is often not applicable in real-world problems. For example, the agent may need to ask a human to supervise its actions or activate a monitoring system to receive feedback. There may even be a period of time before rewards become observable, or a period of time after which rewards are no longer given. In other words, there are cases where the environment generates rewards in response to the agent's actions but the agent cannot observe them. In this paper, we formalize a novel but general RL framework - Monitored MDPs - where the agent cannot always observe rewards. We discuss the theoretical and practical consequences of this setting, show challenges raised even in toy environments, and propose algorithms to begin to tackle this novel setting. This paper introduces a powerful new formalism that encompasses both new and existing problems and lays the foundation for future research.

Mixed-motive multi-agent settings are rife with persistent free-riding because individual effort benefits all members equally, yet each member bears the full cost of their own contribution. Classical work by Holmström established that under pure self-interest, Nash equilibrium is universal shirking. While i* represents teams as composite actors, it lacks scalable computational mechanisms for analyzing how collective action problems emerge and resolve in coopetitive settings. This technical report extends computational foundations for strategic coopetition to team-level dynamics, building on companion work formalizing interdependence/complementarity (arXiv:2510.18802) and trust dynamics (arXiv:2510.24909). We develop loyalty-moderated utility functions with two mechanisms: loyalty benefit (welfare internalization plus intrinsic contribution satisfaction) and cost tolerance (reduced effort burden for loyal members). We integrate i* structural dependencies through dependency-weighted team cohesion, connecting member incentives to team-level positioning. The framework applies to both human teams (loyalty as psychological identification) and multi-agent systems (alignment coefficients and adjusted cost functions). Experimental validation across 3,125 configurations demonstrates robust loyalty effects (15.04x median effort differentiation). All six behavioral targets achieve thresholds: free-riding baseline (96.5%), loyalty monotonicity (100%), effort differentiation (100%), team size effect (100%), mechanism synergy (99.5%), and bounded outcomes (100%). Empirical validation using published Apache HTTP Server (1995-2023) case study achieves 60/60 points, reproducing contribution patterns across formation, growth, maturation, and governance phases. Statistical significance confirmed at p<0.001, Cohen's d=0.71.

The escalating demand for Machine Learning (ML) training resources in recent years has resulted in a substantial gap between the high demand and the available supply. Efficient allocation of these scarce and expensive resources is crucial for organizations to maximize their return on investment. Existing resource allocation mechanisms, like Karma [OSDI'23], are designed to guarantee Pareto efficiency and max-min fairness in settings with dynamic (time-varying) user demands, but fail to preserve these key properties in the presence of demands with heterogeneous values. Given the ubiquity and inevitability of heterogeneity in organizational values of different workloads, effective resource allocation policies must accommodate these variations. In this paper, we describe the design, implementation, deployment, and theoretical analysis of Quota Marketplace, a market-based mechanism to efficiently allocate ML training chips (like GPUs), explicitly addressing scenarios with demands of heterogeneous value. We detail the implementation of this mechanism within Google and present metrics that demonstrate its impact. We also discuss many business-critical requirements that the Quota Marketplace handles quite effectively, and document the gains and opportunities it has unlocked. We establish theoretically how this market-based approach achieves the essential properties of Pareto efficiency and max-min fairness by allowing the users to express the value of their workloads and enabling dynamic resource pricing based on supply and demand fluctuations. Ultimately, the market facilitates resource allocation that aligns with organizational priorities.

Recent advancements adopt online reinforcement learning (RL) from LLMs to text-to-image rectified flow diffusion models for reward alignment. The use of group-level rewards successfully aligns the model with the targeted reward. However, it faces challenges including low efficiency, dependency on stochastic samplers, and reward hacking. The problem is that rectified flow models are fundamentally different from LLMs: 1) For efficiency, online image sampling takes much more time and dominates the time of training. 2) For stochasticity, rectified flow is deterministic once the initial noise is fixed. Aiming at these problems and inspired by the effects of group-level rewards from LLMs, we design Group-level Direct Reward Optimization (GDRO). GDRO is a new post-training paradigm for group-level reward alignment that combines the characteristics of rectified flow models. Through rigorous theoretical analysis, we point out that GDRO supports full offline training that saves the large time cost for image rollout sampling. Also, it is diffusion-sampler-independent, which eliminates the need for the ODE-to-SDE approximation to obtain stochasticity. We also empirically study the reward hacking trap that may mislead the evaluation, and involve this factor in the evaluation using a corrected score that not only considers the original evaluation reward but also the trend of reward hacking. Extensive experiments demonstrate that GDRO effectively and efficiently improves the reward score of the diffusion model through group-wise offline optimization across the OCR and GenEval tasks, while demonstrating strong stability and robustness in mitigating reward hacking.

Reward design is a fundamental, yet challenging aspect of practical reinforcement learning (RL). For simple tasks, researchers typically handcraft the reward function, e.g., using a linear combination of several reward factors. However, such reward engineering is subject to approximation bias, incurs large tuning cost, and often cannot provide the granularity required for complex tasks. To avoid these difficulties, researchers have turned to reinforcement learning from human feedback (RLHF), which learns a reward function from human preferences between pairs of trajectory sequences. By leveraging preference-based reward modeling, RLHF learns complex rewards that are well aligned with human preferences, allowing RL to tackle increasingly difficult problems. Unfortunately, the applicability of RLHF is limited due to the high cost and difficulty of obtaining human preference data. In light of this cost, we investigate learning reward functions for complex tasks with less human effort; simply by ranking the importance of the reward factors. More specifically, we propose a new RL framework -- HERON, which compares trajectories using a hierarchical decision tree induced by the given ranking. These comparisons are used to train a preference-based reward model, which is then used for policy learning. We find that our framework can not only train high performing agents on a variety of difficult tasks, but also provide additional benefits such as improved sample efficiency and robustness. Our code is available at https://github.com/abukharin3/HERON.

We study a class of reinforcement learning problems where the reward signals for policy learning are generated by a discriminator that is dependent on and jointly optimized with the policy. This interdependence between the policy and the discriminator leads to an unstable learning process because reward signals from an immature discriminator are noisy and impede policy learning, and conversely, an untrained policy impedes discriminator learning. We call this learning setting Internally Rewarded Reinforcement Learning (IRRL) as the reward is not provided directly by the environment but internally by the discriminator. In this paper, we formally formulate IRRL and present a class of problems that belong to IRRL. We theoretically derive and empirically analyze the effect of the reward function in IRRL and based on these analyses propose the clipped linear reward function. Experimental results show that the proposed reward function can consistently stabilize the training process by reducing the impact of reward noise, which leads to faster convergence and higher performance compared with baselines in diverse tasks.

Reward guidance has been applied to great success in the test-time adaptation of continuous diffusion models; it updates each denoising step using the gradients from a downstream reward model. We study reward guidance for discrete diffusion language models, where one cannot differentiate through the natural outputs of the model because they are discrete tokens. Existing approaches either replace these discrete tokens with continuous relaxations, or employ techniques like the straight-through estimator. In this work, we show the downsides of both these methods. The former degrades gradient feedback because the reward model has never been trained with continuous inputs. The latter involves incorrect optimization because the gradient evaluated at discrete tokens is used to update continuous logits. Our key innovation is to go beyond this tradeoff by introducing a novel mechanism called EntRGi: Entropy aware Reward Guidance that dynamically regulates the gradients from the reward model. By modulating the continuous relaxation using the model's confidence, our approach substantially improves reward guidance while providing reliable inputs to the reward model. We empirically validate our approach on a 7B-parameter diffusion language model across 3 diverse reward models and 3 multi-skill benchmarks, showing consistent improvements over state-of-the-art methods.

Finding meaningful and accurate dense rewards is a fundamental task in the field of reinforcement learning (RL) that enables agents to explore environments more efficiently. In traditional RL settings, agents learn optimal policies through interactions with an environment guided by reward signals. However, when these signals are sparse, delayed, or poorly aligned with the intended task objectives, agents often struggle to learn effectively. Dense reward functions, which provide informative feedback at every step or state transition, offer a potential solution by shaping agent behavior and accelerating learning. Despite their benefits, poorly crafted reward functions can lead to unintended behaviors, reward hacking, or inefficient exploration. This problem is particularly acute in complex or high-dimensional environments where handcrafted rewards are difficult to specify and validate. To address this, recent research has explored a variety of approaches, including inverse reinforcement learning, reward modeling from human preferences, and self-supervised learning of intrinsic rewards. While these methods offer promising directions, they often involve trade-offs between generality, scalability, and alignment with human intent. This proposal explores several approaches to dealing with these unsolved problems and enhancing the effectiveness and reliability of dense reward construction in different RL applications.

Specifying rewards for reinforcement learned (RL) agents is challenging. Preference-based RL (PbRL) mitigates these challenges by inferring a reward from feedback over sets of trajectories. However, the effectiveness of PbRL is limited by the amount of feedback needed to reliably recover the structure of the target reward. We present the PRIor Over Rewards (PRIOR) framework, which incorporates priors about the structure of the reward function and the preference feedback into the reward learning process. Imposing these priors as soft constraints on the reward learning objective reduces the amount of feedback required by half and improves overall reward recovery. Additionally, we demonstrate that using an abstract state space for the computation of the priors further improves the reward learning and the agent's performance.

Reinforcement learning (RL) holds significant promise for training LLM agents to handle complex, goal-oriented tasks that require multi-step interactions with external environments. However, a critical challenge when applying RL to these agentic tasks arises from delayed rewards: feedback signals are typically available only after the entire task is completed. This makes it non-trivial to assign delayed rewards to earlier actions, providing insufficient guidance regarding environmental constraints and hindering agent training. In this work, we draw on the insight that the ultimate completion of a task emerges from the cumulative progress an agent makes across individual steps. We propose Stepwise Progress Attribution (SPA), a general reward redistribution framework that decomposes the final reward into stepwise contributions, each reflecting its incremental progress toward overall task completion. To achieve this, we train a progress estimator that accumulates stepwise contributions over a trajectory to match the task completion. During policy optimization, we combine the estimated per-step contribution with a grounding signal for actions executed in the environment as the fine-grained, intermediate reward for effective agent training. Extensive experiments on common agent benchmarks (including Webshop, ALFWorld, and VirtualHome) demonstrate that SPA consistently outperforms the state-of-the-art method in both success rate (+2.5\% on average) and grounding accuracy (+1.9\% on average). Further analyses demonstrate that our method remarkably provides more effective intermediate rewards for RL training. Our code is available at https://github.com/WangHanLinHenry/SPA-RL-Agent.

A common approach for aligning language models to human preferences is to first learn a reward model from preference data, and then use this reward model to update the language model. We study two closely related problems that arise in this approach. First, any monotone transformation of the reward model preserves preference ranking; is there a choice that is ``better'' than others? Second, we often wish to align language models to multiple properties: how should we combine multiple reward models? Using a probabilistic interpretation of the alignment procedure, we identify a natural choice for transformation for (the common case of) rewards learned from Bradley-Terry preference models. This derived transformation has two important properties. First, it emphasizes improving poorly-performing outputs, rather than outputs that already score well. This mitigates both underfitting (where some prompts are not improved) and reward hacking (where the model learns to exploit misspecification of the reward model). Second, it enables principled aggregation of rewards by linking summation to logical conjunction: the sum of transformed rewards corresponds to the probability that the output is ``good'' in all measured properties, in a sense we make precise. Experiments aligning language models to be both helpful and harmless using RLHF show substantial improvements over the baseline (non-transformed) approach.

Reinforcement Learning (RL) has enabled Large Language Models (LLMs) to achieve remarkable reasoning in domains like mathematics and coding, where verifiable rewards provide clear signals. However, extending this paradigm to financial decision is challenged by the market's stochastic nature: rewards are verifiable but inherently noisy, causing standard RL to degenerate into reward hacking. To address this, we propose Trade-R1, a model training framework that bridges verifiable rewards to stochastic environments via process-level reasoning verification. Our key innovation is a verification method that transforms the problem of evaluating reasoning over lengthy financial documents into a structured Retrieval-Augmented Generation (RAG) task. We construct a triangular consistency metric, assessing pairwise alignment between retrieved evidence, reasoning chains, and decisions to serve as a validity filter for noisy market returns. We explore two reward integration strategies: Fixed-effect Semantic Reward (FSR) for stable alignment signals, and Dynamic-effect Semantic Reward (DSR) for coupled magnitude optimization. Experiments on different country asset selection demonstrate that our paradigm reduces reward hacking, with DSR achieving superior cross-market generalization while maintaining the highest reasoning consistency.

Building systems that are good for society in the face of complex societal effects requires a dynamic approach. Recent approaches to machine learning (ML) documentation have demonstrated the promise of discursive frameworks for deliberation about these complexities. However, these developments have been grounded in a static ML paradigm, leaving the role of feedback and post-deployment performance unexamined. Meanwhile, recent work in reinforcement learning has shown that the effects of feedback and optimization objectives on system behavior can be wide-ranging and unpredictable. In this paper we sketch a framework for documenting deployed and iteratively updated learning systems, which we call Reward Reports. Taking inspiration from various contributions to the technical literature on reinforcement learning, we outline Reward Reports as living documents that track updates to design choices and assumptions behind what a particular automated system is optimizing for. They are intended to track dynamic phenomena arising from system deployment, rather than merely static properties of models or data. After presenting the elements of a Reward Report, we discuss a concrete example: Meta's BlenderBot 3 chatbot. Several others for game-playing (DeepMind's MuZero), content recommendation (MovieLens), and traffic control (Project Flow) are included in the appendix.

We consider algorithms for learning reward functions from human preferences over pairs of trajectory segments, as used in reinforcement learning from human feedback (RLHF). Most recent work assumes that human preferences are generated based only upon the reward accrued within those segments, or their partial return. Recent work casts doubt on the validity of this assumption, proposing an alternative preference model based upon regret. We investigate the consequences of assuming preferences are based upon partial return when they actually arise from regret. We argue that the learned function is an approximation of the optimal advantage function, A^*_r, not a reward function. We find that if a specific pitfall is addressed, this incorrect assumption is not particularly harmful, resulting in a highly shaped reward function. Nonetheless, this incorrect usage of A^*_r is less desirable than the appropriate and simpler approach of greedy maximization of A^*_r. From the perspective of the regret preference model, we also provide a clearer interpretation of fine tuning contemporary large language models with RLHF. This paper overall provides insight regarding why learning under the partial return preference model tends to work so well in practice, despite it conforming poorly to how humans give preferences.

Reinforcement learning typically optimizes average reward. For generative policies, the average can hide an important distinction: two policies can achieve the same mean reward while having very different chances of producing a rare but high-reward rollout. This matters as sampling increases during training and inference, since its benefit depends on retaining probability mass on high-reward outcomes. We propose to optimize this coverage directly. Rather than considering only expected reward, we consider all of its upper tails: for each reward threshold, how likely is the policy to exceed it? This turns a continuous reward into a family of binary success events. We introduce Tail-Likelihood Reinforcement Learning (TailRL), which maximizes the log-probability of exceeding a randomly chosen reward threshold. Its gradient gives more weight to rare, high-reward rollouts and can be interpreted as a mixture of Best-of-(k) gradients. TailRL requires only a simple modification to the advantage function, making it compatible with existing reinforcement learning pipelines. Across object localization, maze navigation, GUI grounding, and code optimization, TailRL leverages rare high-reward training samples to avoid suboptimal solutions and yields models that benefit more from additional samples at inference time.

Reward Models, essential for guiding Large Language Model optimization, are typically trained on fixed preference datasets, resulting in rigid alignment to single, implicit preference distributions. This prevents adaptation to diverse real-world needs-from conciseness in one task to detailed explanations in another. The standard practice of collecting task-specific preference data and retraining reward models is resource-intensive, often producing biased rewards, and limits practical application. We introduce generalizable, principle-following reward models. We propose that RMs should understand and adhere to dynamically provided natural language specifications of reward principles, similar to instruction-following in LLMs. To measure this capability, we develop RABench, a comprehensive benchmark for RMs focusing on generalization across diverse principles. Evaluations on RABench reveal poor generalization of current RMs. As a solution, we present RewardAnything, a novel RM designed and trained to explicitly follow natural language principles. We achieve SotA performance with RewardAnything in traditional RM benchmark simply by specifying a well-defined principle, and results on RABench show we excel in adapting to novel principles without retraining. Furthermore, RewardAnything integrates seamlessly with existing RLHF methods and we show by a case study on how to automatically and efficiently align LLMs with only natural language principles.

In this report, we introduce a collection of methods to enhance reward modeling for LLMs, focusing specifically on data-centric techniques. We propose effective data selection and filtering strategies for curating high-quality open-source preference datasets, culminating in the Skywork-Reward data collection, which contains only 80K preference pairs -- significantly smaller than existing datasets. Using this curated dataset, we developed the Skywork-Reward model series -- Skywork-Reward-Gemma-27B and Skywork-Reward-Llama-3.1-8B -- with the former currently holding the top position on the RewardBench leaderboard. Notably, our techniques and datasets have directly enhanced the performance of many top-ranked models on RewardBench, highlighting the practical impact of our contributions in real-world preference learning applications.

Reinforcement learning with verifiable rewards (RLVR) enables language models to learn multi-turn interaction with external tools, yet its sparse outcome rewards provide no signal for identifying which intermediate decisions are responsible for success. Branch sampling induces local comparisons among alternative continuations, but existing methods tend to conflate two distinct problems: allocating a fixed rollout budget and translating branch outcomes into token-level credit. We introduce Contrastive Branch Policy Optimization (CBPO), which disentangles these two problems and assigns a dedicated mechanism to each. Generation entropy screens candidate branch positions across the entire response, while path-level and node-level decay distribute a fixed budget across trajectories and positions to prevent exploration from collapsing onto a few paths or adjacent tokens. A parent trajectory together with the branches that share an identical token prefix forms an exact-prefix group, and the reward variation within this controlled group defines the Contrastive Branch Value (CBV), an outcome-based estimate of local decision sensitivity that rescales continuation advantages without altering their sign. When multiple nodes are selected along the same trajectory, CBPO partitions it into non-overlapping credit segments, thereby avoiding duplicated gradients on shared tokens. Requiring only outcome rewards and no process-level annotation, CBPO provides a practical solution for fine-grained credit assignment in tool-integrated agent training. Extensive experiments on ten benchmarks, including five for mathematical reasoning and five for knowledge-intensive search, show that CBPO consistently outperforms state-of-the-art policy-optimization and branch-based methods, attaining the highest macro-average accuracy in both domains and across two model scales.

Diffusion models achieve state-of-the-art generative performance but are fundamentally bottlenecked by their slow, iterative sampling process. While diffusion distillation techniques enable high-fidelity, few-step generation, traditional objectives often restrict the student's performance by anchoring it solely to the teacher. Recent approaches have attempted to break this ceiling by integrating Reinforcement Learning (RL), typically through a simple summation of distillation and RL objectives. In this work, we propose a novel paradigm by re-conceptualizing distribution matching as a reward, denoted as R_dm. This unified perspective bridges the algorithmic gap between Diffusion Matching Distillation (DMD) and RL, providing several primary benefits. (1) Enhanced Optimization Stability: We introduce Group Normalized Distribution Matching (GNDM), which adapts standard RL group normalization to stabilize R_dm estimation. By leveraging group-mean statistics, GNDM establishes a more robust and effective optimization direction. (2) Seamless Reward Integration: Our reward-centric formulation inherently supports adaptive weighting mechanisms, allowing for the fluid combination of DMD with external reward models. (3) Improved Sampling Efficiency: By aligning with RL principles, the framework readily incorporates Importance Sampling (IS), leading to a significant boost in sampling efficiency. Extensive experiments demonstrate that GNDM outperforms vanilla DMD, reducing the FID by 1.87. Furthermore, our multi-reward variant, GNDMR, surpasses existing baselines by striking an optimal balance between aesthetic quality and fidelity, achieving a peak HPS of 30.37 and a low FID-SD of 12.21. Ultimately, R_dm provides a flexible, stable, and efficient framework for real-time, high-fidelity synthesis. Codes are coming soon.

Existing alignment methods share a common topology of information flow, where reward information is collected from humans, modeled with preference learning, and used to tune language models. However, this shared topology has not been systematically characterized, nor have its alternatives been thoroughly explored, leaving the problems of low data efficiency and unreliable generalization unaddressed. As a solution, we introduce a theoretical framework for investigating reward generalization in reinforcement learning from human feedback (RLHF), focusing on the topology of information flow at both macro and micro levels. At the macro level, we portray the RLHF information flow as an autoencoding process over behavior distributions, formalizing the RLHF objective of distributional consistency between human preference and model behavior. At the micro level, we present induced Bayesian networks as a theory of reward generalization in RLHF, introducing fine-grained dataset topologies into generalization bounds. Combining analysis on both levels, we propose reward modeling from tree-structured preference information. It is shown to reduce reward uncertainty by up to Theta(log n/loglog n) times compared to baselines, where n is the dataset size. Validation on three NLP tasks shows that our tree-based reward model achieves an average win rate of 65% against baseline methods, thus improving reward generalization for free via topology design.

Reinforcement fine-tuning (RFT) often suffers from reward over-optimization, where a policy model hacks the reward signals to achieve high scores while producing low-quality outputs. Our theoretical analysis shows that the key lies in reward misspecification at the high-reward tail: the inability to reliably distinguish Excellent responses from merely Great ones. This motivate us to focus on the high-reward region. However, such tail examples are scarce under the base LLM. While off-policy exemplars (e.g. from stronger models or rewrites) are easier to obtain, naively training on them yields a misspecified reward for the policy we aim to align. To address this, we study rubric-based rewards. By design, rubrics can leverage off-policy examples while remaining insensitive to their artifacts. To elicit rubrics that capture the high-reward tail, we highlight the importance of distinguishing among great and diverse responses, and introduce a workflow to implement this idea. We empirically demonstrate that rubric-based rewards substantially mitigate reward over-optimization and deliver effective LLM post-training improvements. Our code can be accessed at https://github.com/Jun-Kai-Zhang/rubrics.git .

Reward models are crucial for aligning large language models (LLMs) with human values and intentions. Existing approaches follow either Generative (GRMs) or Discriminative (DRMs) paradigms, yet both suffer from limitations: GRMs typically demand costly point-wise supervision, while DRMs produce uncalibrated relative scores that lack probabilistic interpretation. To address these challenges, we introduce a novel reward modeling paradigm: Probabilistic Reward Model (PRM). Instead of modeling reward as a deterministic scalar, our approach treats it as a random variable, learning a full probability distribution for the quality of each response. To make this paradigm practical, we present its closed-form, discrete realization: the Ordinal Probabilistic Reward Model (OPRM), which discretizes the quality score into a finite set of ordinal ratings. Building on OPRM, we propose a data-efficient training strategy called Region Flooding Tuning (RgFT). It enables rewards to better reflect absolute text quality by incorporating quality-level annotations, which guide the model to concentrate the probability mass within corresponding rating sub-regions. Experiments on various reward model benchmarks show that our method improves accuracy by 2.9%sim7.4% compared to prior reward models, demonstrating strong performance and data efficiency. Analysis of the score distribution provides evidence that our method captures not only relative rankings but also absolute quality.

Large language models (LLMs) are increasingly trained with reinforcement learning (RL) as autonomous agents that reason and act over long horizons in interactive environments. However, sparse and sometimes unverifiable rewards make temporal credit assignment extremely challenging. Recent work attempts to integrate process supervision into agent learning but suffers from biased annotation, reward hacking, high-variance from overly fine-grained signals or failtures when state overlap is rare. We therefore introduce Online Process Reward Learning (OPRL), a general credit-assignment strategy for agentic RL that integrates seamlessly with standard on-policy algorithms without relying on additional rollouts or explicit step labels. In OPRL, we optimize an implicit process reward model (PRM) alternately with the agent's policy to transform trajectory preferences into implicit step rewards through a trajectory-based DPO objective. These step rewards are then used to compute step-level advantages, which are combined with episode-level advantages from outcome rewards for policy update, creating a self-reinforcing loop. Theoretical findings guarantee that the learned step rewards are consistent with trajectory preferences and act as potential-based shaping rewards, providing bounded gradients to stabilize training. Empirically, we evaluate OPRL on three distinct agent benmarks, including WebShop and VisualSokoban, as well as open-ended social interactions with unverfiable rewards in SOTOPIA. Crucially, OPRL shows superior performance over frontier LLMs and strong RL baselines across domains, achieving state-of-the-art results with higher sample-efficiency and lower variance during training. Further analysis also demonstrates the efficient exploration by OPRL using fewer actions, underscoring its potential for agentic learning in real-world scenarios.

Reinforcement learning has become a cornerstone for enhancing the reasoning capabilities of Large Language Models, where group-based approaches such as GRPO have emerged as efficient paradigms that optimize policies by leveraging intra-group performance differences. However, these methods typically rely on absolute numerical rewards, introducing intrinsic limitations. In verifiable tasks, identical group evaluations often result in sparse supervision, while in open-ended scenarios, the score range instability of reward models undermines advantage estimation based on group means. To address these limitations, we propose Reinforcement Learning with Relative Rewards (RLRR), a framework that shifts reward shaping from absolute scoring to relative ranking. Complementing this framework, we introduce the Ranking Reward Model, a listwise preference model tailored for group-based optimization to directly generate relative rankings. By transforming raw evaluations into robust relative signals, RLRR effectively mitigates signal sparsity and reward instability. Experimental results demonstrate that RLRR yields consistent performance improvements over standard group-based baselines across reasoning benchmarks and open-ended generation tasks.