Reinforcement Learning with Verifiable Rewards

Also known as RLVR

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59 papers in the last four weeks, up 119% on the four weeks before. 0.6% of all new papers.

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Latest papers 438

Aug 22, 2026cs.AI

Training Needs Trustworthy Worlds: Verified Synthetic Web Environments for Agent Learning

Web agents promise to automate complex digital workflows, but their training remains limited by synthetic environments that look plausible while hiding broken links, inconsistent states, or infeasible tasks. We address the gap between scalable environment generation and trustworthy agent learning by constructing synthetic web environments that are executable, auditable, and grounded in backend state. Our framework represents each generated website as a structured scaffold of pages, navigation links, database records, state-change markers, and task constraints, then verifies and repairs structural, semantic, consistency, and feasibility defects before policy training. During interaction, ordinary UI transitions are executed deterministically, while persistent backend updates are invoked only through validated state-change markers, enabling dense rewards compiled from verified task-progress predicates. Across 500 synthetic environments spanning six domains, our method reduces task-blocking defects and improves feasible-task rate from 48.6% to 94.8%, while producing stronger PPO policies and improving transfer to WebArena, WebShop, and MiniWoB++ without LLM calls at evaluation time. These results show that verified synthetic environments can serve as a scalable and reliable training substrate for compact web agents, shifting synthetic webagent learning from surface-level plausibility toward executable, state-grounded supervision.

Chenghao Zhang, Yuxi Cheng, Saisai Hu +3

University of Pennsylvania · Pace University · Shenzhen Campus of Sun Yat-sen University

Reinforcement Learning with Verifiable Rewards Web Agents

Aug 19, 2026cs.LG

Beyond Forgetting: Diagnosing and Harnessing Shared Reasoning in Continual RLVR

Reinforcement learning with verifiable rewards (RLVR) commonly post-trains reasoning models on multiple tasks, while rerunning multitask RLVR (MTRL) as new tasks are added makes capability expansion costly. We therefore study continual RLVR, which updates the existing model as each task arrives. The central question is whether a model updated this way can perform as well as a jointly trained model. To answer this question, we introduce Continual Reasoning Gym, a continual-RLVR environment that organizes text and visual reasoning tasks into five task sequences. In this setting, we identify two key observations: Sequential RLVR exhibits modest forgetting, yet its final performance remains below that of MTRL. To understand the latter, we decompose final performance and show that forgetting accounts for only part of the gap. To explain the former, we identify shared reasoning: transferable reasoning structure allows training on one task to support others on average. We therefore introduce Continual Prompt Replay (CPR), which harnesses shared reasoning to improve learning on the arriving and future tasks by replaying previous-task prompts and regenerating their responses with the current policy. On average, only CPR reaches MTRL-level performance.

Lirui Luo, Guoxi Zhang, Hongming Xu +3

State Key Lab of General AI, School of Intelligence Science and Technology, Peking University · State Key Laboratory of General Artificial Intelligence, BIGAI · Beijing Institute of Technology +1

RL for Language Model Reasoning Replay-Based Continual Learning Transfer Learning Reinforcement Learning with Verifiable Rewards Continual RL

Aug 13, 2026cs.AI

Teach the Magnitude, Not the Direction: Verifier-Bounded Credit Assignment for Multi-Turn Multi-step LLM Agents

Reinforcement learning with verifiable rewards (RLVR) offers a verifier-bounded performance ceiling for training multi-turn tool-use agents, yet its trajectory-level credit assignment conflates heterogeneous per-turn outcomes into a single reward signal. On-policy distillation provides dense per-token supervision but is either teacher-bounded or prone to gradient concentration collapse. We introduce

\textbf{CrEST}

, a hierarchical credit assignment framework that retains RL's verifier-bounded ceiling while incorporating dense token-level signals from a privileged self-teacher.

\textbf{CrEST}

resolves credit at two levels: turn-segmented verified advantages address inter-turn dilution, while entropy-gated self-teacher modulation refines intra-turn token contributions. Experiments on BFCL V3 and WildToolBench show that

\textbf{CrEST}

consistently outperforms both RL and distillation baselines across two model scales, with the largest gains on long-trajectory and strict session-level metrics. Our work demonstrates that the teacher's role in policy optimization can be reduced from determining update directions to modulating update magnitudes, unlocking dense credit assignment without sacrificing the verifier-bounded ceiling.

Zechuan Wang, Siyuan Lu, Hongxuan Zhang +3

Zhejiang University · AWorld Team, Inclusion AI · Shanghai Innovation Institute +2

Token-Level Credit Assignment Step-Level Credit Assignment in RL Reinforcement Learning with Verifiable Rewards Step-Level Credit Assignment On-Policy Distillation RL for Tool Use

Aug 11, 2026cs.LG

PAIR: Pairwise-Aware Inclusion Reweighting for Adaptive Rollout Allocation in RLVR

Reinforcement learning with verifiable rewards (RLVR) spends most of its compute generating groups of long reasoning trajectories. Recent allocators reduce this cost by assigning budgets to prompts, rollouts, or tokens according to a pointwise notion of difficulty or utility. We identify a statistical mismatch: the unclipped leave-one-out group-relative score gradient is not a sum of independent point contributions, but a second-order U-statistic over pairs of rollouts. Completing one rollout therefore reveals contrast with every other completed rollout, and adaptive endpoint selection changes which pair terms are observable. We introduce PAIR (Pairwise-Aware Inclusion Reweighting), which treats short rollout prefixes as vertices and pair-gradient terms as edges of a contrast graph. A prefix-only predictor estimates correctness and remaining token cost; a convex design chooses positive continuation probabilities under an expected suffix-token budget; and each edge induced by completed vertices is inverse-weighted by its logged joint inclusion probability. Under conditionally independent on-policy rollouts and an unclipped, unstandardized objective, the resulting estimator is design-unbiased for the complete candidate-pair gradient. Across compute-matched RLVR runs on Qwen3-1.7B/4B, PAIR improves average accuracy by +1.2 and +1.4 over the strongest pointwise allocator while using 51% and 52% fewer generated tokens than full-group GRPO. A frozen-population estimator audit confirms that unweighted adaptive selection is biased, whereas pair-inclusion correction recovers the complete-pair target at matched suffix cost.

Pixel Nomand, Elena Voss, Marcus Hale +1

University of Wisconsin–Madison · University of Washington

Inverse Probability Weighting Reinforcement Learning RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards

Aug 11, 2026cs.CL

ConRub-Med: Reinforcement Learning with Consensus Rubrics for Open-Ended Medical Question Answering

Reinforcement learning with verifiable rewards has been especially effective in mathematics and coding, where answers can be checked automatically. Many open-ended medical questions lack comparably cheap outcome verifiers: responses may be partly correct, incomplete, or contain clinically consequential errors. Rubrics written or validated by physicians offer strong clinical grounding, but involving experts in every instance is costly. Model-generated rubrics make this supervision scalable. We introduce ConRub-Med to preserve useful distinctions as rubric feedback moves from construction to policy optimization. For each prompt, three heterogeneous language models propose atomic criteria independently; a separate model reviews them, retaining only criteria with semantic support from all three generators. Three-State scoring distinguishes correct coverage, missing information, and incorrect claims. Errors receive negative rather than zero credit. When every response in a complete Group Relative Policy Optimization (GRPO) group receives the same final reward, a pairwise judge provides sequence advantages only if both candidate orders agree, without changing the scalar rewards. Groups without ties use vanilla GRPO. In a blinded study matched by question, two medical experts rate panels from the full pipeline as more clinically relevant than panels produced by one generator. Across the evaluated open models, ConRub-Med ranks first on six of nine benchmarks and achieves the highest medical and generalization averages. Using the resulting rubric dataset of 5,166 prompts, it scores

38.98 \pm 1.04

(mean

\pm

SD) on HealthBench-Hard, compared with InfiMed-ORBIT's 33.60 with 8,000 samples and 37.30 with 28,000.

Taojie Zhu, Yuan Xia, Tao Sun +8

Tsinghua University · Ant Group · Zhejiang University

Rubric-Based RL Medical QA Reinforcement Learning with Verifiable Rewards Rubric-Guided Generation

Aug 11, 2026cs.CL

Dual-Loop Self-Evolution via Verifiable Emotion Feedback for Multi-Turn Empathetic Dialogue

Large language models have demonstrated conversational capabilities, yet empathetic competence remains challenging. Empathetic support is inherently multi-turn and path-dependent: users disclose concerns gradually, emotions evolve over time, and early responses shape trust and receptivity. Reinforcement learning with verifiable emotion rewards provides scalable supervision for long-horizon interactions. However, existing methods evolve the dialogue policy while keeping its training interaction distribution fixed, creating a mismatch between policy competence and training experience. We introduce a dual-loop self-evolution framework driven by verifiable emotion feedback. With the user simulator and verifier frozen, the inner loop optimizes the multi-turn policy using continuous emotion rewards, while the outer loop uses the same outcomes to estimate policy-relative interaction utility and adapt experience. To obtain estimates from sparse, stochastic rollouts, the framework holds the scenario and interaction state constant within each group and prioritizes conditions whose group pass rates lie near the policy's competence boundary. A hierarchical controller shares evidence across support intents, while uncertainty-guided exploration and uniform rehearsal prevent premature exclusion. The resulting distribution generates trajectories, closing both loops without increasing the rollout budget. On SAGE, our framework raises Qwen3-8B Overall from 53.87 to 79.24 and outperforms protocol-matched uniform emotion-reward reinforcement learning by 7.23 points.

Yi Wei, Shuo Jiang, Huaixia Dou +5

Qwen DianJin Team, Alibaba Cloud Computing · Beihang University · School of Computer Science and Technology, Soochow University

Reinforcement Learning with Verifiable Rewards Curriculum Learning Language Model Self-Improvement Emotion-Aware Dialogue Generation

Aug 10, 2026cs.LG

Distill Skills into Weights, Not Prompts: Abstract Skills as Privileged Signals for On-Policy Self-Distillation

Reinforcement learning with verifiable rewards yields no group-relative signal when rollout groups are uniformly correct or uniformly wrong, which account for 63.0-68.0% of groups in our experiments. We propose SKALD (Skill-Anchored Latent Distillation), an on-policy self-distillation framework that uses two context views of the same Qwen3-Base model: a question-only student and a teacher conditioned on an abstract, explicit-answer-filtered skill card. The student is trained on its own prefixes, transferring the skill-induced advantage into shared parameters without privileged input at test time. To stabilize context-induced distribution mismatch, SKALD employs an annealed exponentially tilted objective that downweights teacher-preferred tokens with very low student likelihood; as the tilt vanishes, it converges to teacher cross-entropy and recovers the forward-KL student gradient. An empirical gate activates distillation only when verified rollouts estimate a positive teacher advantage. Across five held-out mathematics benchmarks, SKALD improves overall avg@8 over GRPO by +2.46, +4.85, and +12.01 at 0.6B, 1.7B, and 4B, respectively. At 1.7B, zero-variance-only distillation recovers 84.7% of the full gain, while SKALD remains +4.06 above FLOP-matched GRPO and exceeds contextual skill exposure by +3.77. These results show that abstract skills provide dense supervision where group-relative rewards become uninformative.

Yubo Jiang, Fengying Xie, Zhiguo Jiang +1

School of Astronautics, Beihang University, Beijing 102206, China · Longcat Interaction Team, Meituan, Beijing 100102, China · Tianmushan Laboratory, Beihang University, Hangzhou 311115, China

On-Policy Self-Distillation RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Learning Using Privileged Information

Aug 10, 2026cs.LG

Parameter Exploration for RLVR via Variational Learning

Exploration has been a focus of reinforcement learning research for a long time. Recently, there has been growing evidence that it is also an important ingredient in LLM reinforcement learning recipes that can significantly impact downstream performance. Many existing methods control exploration in the action-space, for example, using temperature scaling. However, these methods cannot reorder tokens but only influence the variance in the output distribution. This limits exploration and can lead to divergence or stalled training. Here, we investigate parameter-space exploration, where rollouts are generated by sampling different policies from a posterior that may each explore different rollouts. Sampling less or more diverse policies is then a complementary control lever over exploration. We introduce a family of methods called Perturbed Parameter Policy Optimization (3PO) which use different sampling strategies and different rollout grouping for reward estimation. Experiments on OLMo-3-1025-7B and Qwen2.5-Math-7B across mathematical reasoning and code generation tasks show that these approaches consistently improve average downstream performance over standard GRPO at a near-identical FLOPs cost. Moreover, using multiple parameter samples consistently produces fewer zero-advantage groups and malformed or incorrect rollouts during training than GRPO and action-space baselines. Overall, our work presents evidence that parameter-space exploration can improve reinforcement learning for LLMs.

Vatsal Venkatkrishna, Nico Daheim, Iryna Gurevych

INSAIT, Sofia University “St. Kliment Ohridski”, Bulgaria · Ubiquitous Knowledge Processing Lab (UKP Lab), Department of Computer Science, Technical University of Darmstadt and National Research Center for Applied Cybersecurity ATHENE, Germany

RL for Language Model Reasoning RL Exploration Reinforcement Learning with Verifiable Rewards

Aug 10, 2026cs.LG

SoftmaxGRPO: Learning to Reason using Softmax Advantage Group Estimation

Group-based reinforcement learning objectives such as GRPO can allocate learning signal poorly across prompt difficulty: under binary rewards, group normalization induces a divergent weighting on easy prompts. We introduce Softmax Advantage Group Estimation (SoftmaxGRPO), a drop-in alternative that replaces z-score-normalized group advantages with temperature-scaled softmax advantages, keeping weights bounded regardless of prompt difficulty. For binary rewards, we derive the exact finite-group population objective and identify MaxRL as its low-temperature limit. For bounded scalar rewards, we show that the large-group update exactly optimizes a log-moment-generating-function objective, while a universal finite-group scalar objective cannot exist without additional assumptions on the reward distribution. Empirically, SoftmaxGRPO reallocates measured gradient budget away from near-solved prompts and consistently improves over GRPO under identical rewards. It reaches 51.8% on DeepMath with verifiable rewards and improves a 1.5B instruction-tuned model from 35.0% to 68.0% on Poetry using only lightweight text-similarity rewards.

Jefferson Hernandez, Jaywon Koo, Zilin Xiao +2

Rice University

RL for Language Model Reasoning Group Relative Policy Optimization Reinforcement Learning with Verifiable Rewards Policy Learning

Aug 9, 2026cs.AI

LLM Reasoning for Subjective Tasks: Failure Modes, Mitigation, and Dynamic Reasoning Routing

Recommendation systems thrive on personalization, where ''correctness'' is rarely a binary truth but a matter of subjective human preference. As Large Language Models (LLMs) are deployed as autonomous verifiers of safety and quality guidelines, they face a distinctive challenge: context-aware preference alignment. Recent gains in Reinforcement Learning with Verifiable Rewards (RLVR) are indexed mostly on objective, mathematical tasks. Through a large-scale study spanning both proprietary and open-source models on four real-world verification tasks from a production recommender platform, we ask whether explicit reasoning generalizes to subjective, human-centric industry rubrics. We expose a fundamental vulnerability: rigid, math-centric reasoning traces actively degrade verification, and applying standard RLVR triggers a phenomenon we term reasoning collapse, in which the policy abandons deliberation in favor of rapid heuristic guessing. We introduce a conditional length-penalized post-training algorithm that intertwines verification accuracy with bounded reasoning length, halting collapse and recovering performance. Finally, we show that a reasoning trace's efficacy is tightly coupled with its socio-linguistic framing: across 1500 synthesized personas, verification accuracy swings by nearly 0.38 macro-F1 depending solely on the adopted reasoning persona---evidence that much subjective-verification error is really reasoning-style mismatch. This observation motivates a mid-training architecture that routes reasoning through contextually aligned personas. This work offers both a scalable algorithmic patch and a long-term architectural blueprint for aligning reasoning models with real-world subjective constraints.

Juncheng Dong, Ding Tong, Ishan Gupta +1

Duke University · Durham, USA · Netflix +1

Reinforcement Learning with Verifiable Rewards

Aug 9, 2026cs.AI

Improving Generalization Robustness of Multimodal RLVR

Reinforcement Learning with Verifiable Rewards (RLVR) makes Multimodal Large Language Models more accurate, but the gains are brittle: simply paraphrasing a question or changing the prompt template can degrade them, which challenges reliable deployment in high-stakes scenarios like medical VQA. We trace this to two issues of the standard RL objective. First, the binary verifier conflates format with content, so the reward signal cannot tell a wrong answer apart from a misformatted one. Second, the training distribution covers only a thin slice of the real-world prompts that the model might meet at deployment, so policies that perform well on the training distribution can behave differently under unseen prompts during test. Both failures call for a robust post-training method that helps the policy cover a broader distribution of semantically equivalent prompts, and we identify two measures that help achieve this objective: separating format from semantics in the reward, and applying policy invariance across perturbed prompts with equivalent semantics. We therefore propose Prompt-Invariant RLVR (PIRL), consisting of a dynamic trinary reward and a consistency regularizer based on an embedding-space adversary. Under stress testing, PIRL's average accuracy on benchmarks drops by only

\le 1\%

, where GRPO drops ~3%. On dynamic evaluation, PIRL also achieves the smallest performance drop.

Pengfei Zhou, Zhiwei Tang, Xiaopeng Peng +11

1National University of Singapore, HPC-AI Lab · 2DAMO Academy, Alibaba Group · 3Hupan Lab +7

Multimodal Robustness Multimodal Large Language Models Reinforcement Learning with Verifiable Rewards Prompt Robustness

Aug 9, 2026cs.AI

MedCalc-R1: Knowledge-Guided Reward Framework for Medical Mathematical Reasoning

In Reinforcement Learning with Verifiable Rewards (RLVR) frameworks for mathematical reasoning tasks, floating-point results are typically evaluated using a tolerance-based reward. However, this strategy suffers from challenges such as difficulty in threshold calibration, unstable training dynamics, and limited accuracy, especially in clinical scenarios. To address these limitations, we propose a knowledge-guided hybrid reward framework (\textsc{MedCalc-R1}). Specifically, we introduce a knowledge verification reward mechanism that enforces explicit generation of computational formulas, which are further validated by an external verifier to enhance interpretability and reasoning reliability. Furthermore, we design a hybrid soft-hard reward scheme combining a hard constraint based on clinical safety thresholds with a soft, precision-sensitive reward that progressively guides learning within the acceptable range. Experimental results demonstrate that our method significantly outperforms existing baselines in both reasoning accuracy and generalization capability, validating the effectiveness and applicability in safety-critical domains.

Haotian Wang, Lian Yan, Xingzhi Yao +4

Harbin Institute of Technology

Numerical Reasoning in Language Models Reinforcement Learning with Verifiable Rewards Reward Design for RL

Aug 8, 2026cs.AI

StructReward: Efficient Structured Process Rewards for Self-Correcting Multimodal Reasoning

Reinforcement learning with verifiable rewards (RLVR) has emerged as an effective approach for improving multimodal reasoning. However, most existing methods evaluate an entire response using a binary reward based only on final-answer correctness, thereby discarding the supervision available in intermediate reasoning steps. Process reward models offer finer-grained feedback, but they typically rely on separately trained verifiers, costly chain-of-thought annotations, or online judging by large language models (LLMs). In this work, we introduce StructReward, a compute-efficient framework that provides dense reinforcement signals through structured step-level reward alignment. StructReward represents each generated solution as a sequence of reasoning steps and aligns them with process-labeled reference steps using lightweight numerical, symbolic, and lexical matching rules. The aligned labels are aggregated into a dense process reward and combined with final-answer consistency and output-validity rewards through a gated Group Relative Policy Optimization (GRPO) objective. We further recycle policy rollouts into complementary supervision for response comparison and reflective self-correction, rather than discarding them after policy updates. Separately, we use a strong LLM to rewrite sampled correct trajectories into reflection-oriented training instances, further strengthening the policy's ability to evaluate and refine its reasoning. Since reward computation is performed online without an additional learned verifier or external LLM judge, StructReward substantially reduces the computational overhead of multimodal reinforcement learning. Experimental results show that structured process supervision and rollout recycling provide an efficient path toward self-improving multimodal reasoning.

Yifan Li, Ruxin Sun, Tongzhou Zhao

Process Reward Models Multimodal Reasoning Reinforcement Learning with Verifiable Rewards RL for VLMs

Aug 7, 2026cs.AI

DiDPO: Diff-in-Diff Policy Optimization for Coding Agent Training

Reinforcement learning with Verifiable Reward (RLVR) has emerged as a powerful paradigm for training coding agents, where the execution feedback from compilation and tests provides objective verification. However, unlike agent tasks, coding agents face a unique and finer-grained credit assignment challenge: at each step, coding actions simultaneously pack varying changes into different regions of a code version, which makes the contribution of independent change indistinguishable. Existing RLVR methods mostly leverage the outcome reward or step-level reward, which fails to dive into a code diff and makes unique properties of coding actions invisible to training. In this paper, we propose Diff-in-Diff Policy Optimization (DiDPO), a critic-free RL method that constructs fine-grained credit units directly from the structure of code diffs. DiDPO organizes multi-turn coding interactions into multiple thought--action steps and discovers code diffs across sampled trajectories. It then selects anchors by aggregating highly similar sub-diffs split from each whole diff by our ``groupability score'', which provides the splitting schema that optimally balances the semantic scope of anchors and the group mass they may form. Finally these anchors form advantage groups and project the diff-level advantage back to individual response tokens. Experiments on long-horizon coding and reasoning benchmarks show that DiDPO significantly outperforms strong agentic RL baselines. On Qwen2.5-7B-Coder, DiDPO exceeds comparable methods by over 10% and narrows the gap with far larger models, offering a principled framework for fine-grained credit assignment in coding agent training. We also open-source verl-code, an agentic rl codebase that supports various RL methods and coding benchmarks.

Xucong Wang, Zhe Zhao, Liheng Yu +3

University of Science and Technology of China (USTC) · Stanford University · Tongji University +1

RL for Code Generation Credit Assignment in RL Reinforcement Learning with Verifiable Rewards

Aug 6, 2026cs.AI

WebGrader: Training LLMs for Web Development with Self-Evolving Programmatic Grader

Large language models increasingly generate complete websites from natural-language descriptions, and reinforcement learning has become a central approach to closing their remaining functional gap. This training regime is bottlenecked by reward design. Hand-authored browser scripts are executable yet costly to write for open-ended requirements, while VLM and GUI-agent graders scale but may issue verdicts before observing the decisive state. We propose WebGrader, a self-evolving programmatic grader that autonomously derives the required interaction flows from each website request, represents each flow as an executable Flow Contract, and uses its execution outcome as an RL reward. WebGrader materializes the generated project in a live browser, grounds target actions against the source code and live DOM, and collects visual, DOM, response, and persistent-state evidence along the same browser trajectory. A residual-driven offline loop then discovers reusable verifier skills, screens them on disjoint validation pages, and freezes the promoted skill graph before policy training. By separating test planning, action grounding, evidence collection, and semantic judgment, WebGrader issues a Pass verdict only after observing the requested transition. On WebGen-Bench, WebGrader trains an 8B policy to a 52.01% functional success rate, outperforming a matched appearance-plus-script reward by 7.88 points and surpassing o4-mini and DeepSeek-v4-flash. On WG-core-250, the policy reaches a Full Score of 44.953 and surpasses Qwen3-Coder-480B.

Boshui Chen, Huiping Liu, Shaolei Zhang

Beijing Institute of Technology, China · Beijing Jiaotong University, China · Renmin University of China, China

RL for Code Generation Automated Software Testing Web Application Generation Reinforcement Learning with Verifiable Rewards Automated Grading

Aug 6, 2026cs.AI

DASH: Divergence-Adaptive Supervision Horizons for On-Policy Self-Distillation of Reasoning Models

Reinforcement learning with verifiable rewards (RLVR) improves the reasoning capabilities of large language models using automatically verifiable outcome signals, but these signals are typically sparse and at the sequence-level. On-policy self-distillation (OPSD) mitigates this sparsity by querying a privileged teacher at student-visited prefixes and providing dense token-level distributional supervision. Although this dense supervision alleviates signal sparsity, we find that standard OPSD still underexploits the temporal structure of the rollout. It assigns every local divergence the same coefficient, regardless of its position or the divergence sequence in which it occurs. In on-policy autoregressive generation, the same divergence magnitude can follow different discrepancy histories, reflecting different evolutions of the mismatch between the teacher and student. Since the local scalar alone cannot distinguish these temporal contexts, standard OPSD cannot adapt its token-level weights to the realized discrepancy sequence. To address this limitation, we propose Divergence-Adaptive Supervision Horizons (DASH). DASH maps the gap between each local distillation signal and the sequence-level mean to an adaptive propagation gate and then uses these gates to control backward multi-step aggregation. By doing so, DASH adjusts token-level supervision weights according to how local divergences evolve during generation. Experiments on three mathematical reasoning benchmarks across three model scales show that DASH improves over our matched vanilla OPSD reruns on every benchmark at all three scales. DASH reuses the teacher and student distributions that OPSD already computes, so the gains require no additional teacher or student forward pass. Code: https://github.com/DBtxy/DASH-OPSD

ZhiYan Hou, Xinyu Tang, Hongyan An +9

Institute of Automation, Chinese Academy of Sciences · EverMind · Shanda Group +3

On-Policy Self-Distillation RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards On-Policy Distillation LLM Reasoning

Aug 6, 2026cs.AI

AgentOPSD: Recursive Self-Distillation for Agentic Reinforcement Learning

Reinforcement learning (RL) with verifiable rewards constructs trajectory-level advantage estimates, yet it often fails to credit the few pivotal decisions that determine outcomes in long-horizon, multi-turn agentic tasks. Recent work introduces privileged self-distillation for credit assignment, providing denser supervision, but it remains unclear how such local signals should represent sequential credit. We propose AgentOPSD, a critic-free, recursive method for turn-level credit assignment in agentic reinforcement learning. AgentOPSD aggregates token-level teacher-student log-probability gaps into turn-level evidence and recursively updates a Bayesian belief state in log-odds space. This yields a principled reweighting scheme that converts sparse outcome supervision into turn-level credit signals and identifies pivotal turns through the marginal belief revision between consecutive states. The method is fully compatible with standard policy optimization and requires neither an additional critic nor extra rollouts. We evaluate AgentOPSD on ALFWorld, WebShop, and Search-QA using Qwen2.5 models at two scales (3B and 7B). AgentOPSD outperforms GRPO and strong self-distillation baselines, achieving 89.1% success on ALFWorld with Qwen2.5-7B. Ablation studies attribute the gains to turn-level aggregation and history-dependent recursive belief updates.

Zi-Han Wang, Zhengxi Lu, Zhiyuan Yao +10

Tsinghua University · Meituan · Zhejiang University

Agentic RL Reinforcement Learning Credit Assignment in RL Step-Level Credit Assignment in RL Reinforcement Learning with Verifiable Rewards Policy Learning

Aug 5, 2026cs.AI

WorldCycle: Self-Verifiable Reinforcement Learning for Long-Horizon Video World Models

Interactive video world models are essential for long-horizon planning and exploration, yet they suffer from compounding errors. Post-training methods such as reinforcement learning (RL) can improve these models, but they hit a verification bottleneck: for arbitrary action sequences, no ground-truth future state exists to measure long-term drift. Our key insight is that reversible action cycles make this verification possible: a sequence composed with its inverse must analytically return to the initial state, yielding annotation-free supervision on long-horizon correctness. Building on this, we introduce WorldCycle, a self-verifiable RL framework that constructs closed action cycles and their repeated executions from ordinary action sequences, and optimizes two complementary rewards: a spatial closure reward enforcing symmetry between mirrored forward and reverse segments, and a temporal consistency reward aligning states across repeated cycle executions. These rewards force the model to learn actions as consistent state operators rather than memorized temporal patterns, and extend naturally to out-of-distribution composite action cycles that the base model handles poorly. We further release CycleBench, a diagnostic benchmark for state-returning ability under complex action structures. WorldCycle reduces state returning drift by up to 44% and lifts composite-action accuracy nearly 4x over the base model, providing a vital foundation for physically grounded world models.

Bohai Gu, Yueyang Yuan, Taiyi Wu +9

1The Hong Kong University of Science and Technology · 2Wuhan University · 3AI Technology Center, Tencent Video, Tencent

World Model-Based Planning Action-Conditioned World Models Reinforcement Learning with Verifiable Rewards World Model Evaluation Interactive World Models Video World Models

Aug 5, 2026cs.CR

Trident : How to Break Deep Reinforcement Learning Cyber Defenses (Agentic)

Autonomous cyber defense systems based on Deep Reinforcement Learning (DRL) have attracted significant research attention, yet remain evaluated almost exclusively against static, heuristic red agents, leaving their robustness against adaptive threats critically understudied. Meanwhile, recent advances in Reinforcement Learning with Verifiable Rewards (RLVR) have improved LLM reasoning, but their integration into cybersecurity remains elusive due to the absence of suitable benchmark environments and interaction datasets. To bridge this gap, we introduce Trident, an agentic LLM red teaming framework comprising three components: a dynamic benchmark with isolated sandbox servers spanning CybORG CAGE 4 and CyberWheel, a dataset comprises over 13,000 high-fidelity red-blue interaction trajectories for RLVR, and a ``Code-as-Policy'' RLVR agentic architecture Trident Agentic). The latter reformulates red agent training as a contextual bandit via a tripartite Log Summarizer--Planner--Coder design, where a trainable Planner generates complete attack strategies from compressed execution logs, which a frozen Coder translates into executable Python policies deployed against live DRL defenders. Empirical evaluations reveal a fundamental brittleness in existing defenses: with a single trainable 7B planner, Trident reduces blue agent defensive performance by an average of 522% compared to static red agent baselines while autonomously discovering emergent behaviors such as decoy avoidance and adaptive state prioritization that static heuristics entirely fail to uncover.

Ryozo Masukawa, Ian Bryant, Armita Kazeminajafabadi +6

University of California, Irvine · Northeastern University · Johns Hopkins University

Autonomous Cyber Defense LLM Red Teaming AI Agent Security Benchmarks Reinforcement Learning with Verifiable Rewards Automated Red Teaming

Aug 4, 2026cs.AI

When Correct Solutions Repeat: Rarity-Aware Credit Redistribution for GRPO

Reinforcement learning with verifiable rewards (RLVR) com- monly optimizes each correct completion as an independent learning signal. In GRPO, this completion-level uniformity creates structure-level skew: recurring correct solution forms accumulate positive coefficient mass in proportion to how often they are sampled, while rare forms receive limited credit. We formalize this behavior as multiplicity-induced structure-level credit concentration and introduce a partition- conditioned rule that redistributes positive advantages accord- ing to cluster rarity. Cue-GRPO instantiates this rule with- out auxiliary-model inference by using deterministic Strategy Cues to construct rollout-local partitions of verified-correct traces. Across Qwen2.5-Math-7B and Llama-3.1-8B-Instruct, Cue-GRPO improves AIME repeated-sampling performance, with the largest gains at high sampling budgets. Credit Re- distribution (CR) under Judge Partitions (JP) further indi- cates that the proposed redistribution mechanism can oper- ate with judge-derived partitions. Cue-GRPO adds only 6% wall-clock training overhead over GRPO. These results sup- port structure-level credit redistribution as a practical design axis for RLVR, with Strategy Cues providing a low-overhead implementation for competition mathematics. Code is avail- able at https://github.com/CzZ12/When-Correct-Solutions- Repeat-Rarity-Aware-Credit-Redistribution-for-GRPO.

Zhe Cao, Miaowen Wen, Fangjiong Chen

South China University of Technology

RL for Language Model Reasoning Group Relative Policy Optimization Credit Assignment in RL Reinforcement Learning with Verifiable Rewards Credit Assignment

Aug 4, 2026cs.AI

Don't Peek at the Answer: Outcome-Masked Group Relative Policy Optimization for Label-Free RLVR

Reinforcement Learning with Verifiable Rewards (RLVR) improves LLM reasoning but typically relies on ground-truth (GT) answers, limiting scalability. Voting-based label-free RLVR replace gold supervision with answer-level consensus from model samples. However, collapse arises when the same answer-level signal is used both to estimate rewards and to drive token-level policy optimization, encouraging the model to directly reinforce answer tokens rather than improve reasoning. We propose OM-GRPO, a label-free RLVR framework that decouples reward estimation from policy optimization. OM-GRPO masks gradients on the answer span while retaining answer-level rewards through a soft consensus signal, shifting optimization pressure away from answer tokens. We further introduce Contrast-Augmented Reward, which refines reward estimation via low-cost pairwise comparisons over existing trajectories without additional rollouts. Across diverse reasoning benchmarks and three LLM backbones, OM-GRPO consistently outperforms existing label-free RLVR methods and matches supervised GT-reward training with stable optimization. This stability is particularly beneficial in the Test-Time Training setting, where OM-GRPO surpasses majority voting by 4.24 points.

Yongshi Ye, Liang Zhang, Yidong Chen +2

Xiamen University · Key Laboratory of Digital Protection and Intelligent Processing of Intangible Cultural Heritage of Fujian and Taiwan (Xiamen University), Ministry of Culture and Tourism

RL for Language Model Reasoning Group Relative Policy Optimization Reinforcement Learning with Verifiable Rewards

Aug 3, 2026cs.CL

BODHI: Do LLMs Branch Out and Discover Heterogeneous Inferences?

Although reinforcement learning with verifiable rewards (RLVR) has improved the performance of large language models (LLMs) across a variety of reasoning tasks, there is significant debate as to whether RLVR expands the reasoning capability boundary, or just improves sampling efficiency. In this paper, we investigate the nature of test-time exploration in RLVR-trained LLMs by employing controlled maze-solving experiments and extracting a tree structure from mathematical reasoning traces (BODHI-Trees) based on semantic equivalence. This helps us delineate between entropy arising from stylistic variations and genuine inferential branching. Our findings demonstrate that the policy entropy collapse observed in RLVR models is not merely syntactic, and is accompanied by a significant reduction in semantic branching entropy. While RLVR improves adherence to environmental constraints and backtracking capabilities, it constricts the space of continuations; we provide evidence suggesting that this might be responsible for the sample efficiency gains of RLVR, albeit at the cost of genuine rollout diversity.

Soumadeep Saha, Krish Sharma, Akshay Chaturvedi +1

ANITI, Université de Toulouse · LINAGORA Labs

Reasoning Diversity RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards

Aug 3, 2026cs.SD

Reinforcement Learning with Evolving Rubrics as Rewards for Audio Reasoning

Audio reasoning is essential for machine understanding of the acoustic world. Reinforcement learning with verifiable rewards can elicit such reasoning, yet existing reward designs are complementary in their limitations: outcome-based rewards supervise only the final answer and let the model reach it without attending to the audio, whereas process-based rewards score the reasoning itself but rely on coarse, hand-crafted, and fixed criteria that neither adapt to each question nor stay grounded in the acoustic evidence. Moreover, questions differ in what they demand, with some hinging on perception and others on multi-step reasoning, and any static criterion weakens as the policy improves. Supervising the reasoning process with fine-grained, audio-grounded, and adaptive rewards is therefore crucial, yet challenging since such rewards are impractical to design by hand for every sample. To this end, we introduce AudioRubrics, a reinforcement learning framework that supervises audio reasoning with self-evolving, audio-grounded rubric rewards. AudioRubrics synthesizes per-sample rubrics from the raw waveform and, conditioned on the model's own rollouts, regenerates and reweights criteria per group, supplying a continuous learning signal that keeps targeting the current policy's weaknesses as static criteria saturate. Comprehensive evaluations across three audio reasoning benchmarks reveal that AudioRubrics substantially outperforms a wide range of open-source and training-based baselines. Furthermore, our analysis shows that the gains scale with the capability of the rubric generator and judge, and AudioRubrics converges to a stable reasoning length that avoids both degenerate collapse and unbounded growth. The improvement in audio perception further demonstrates the effectiveness of anchoring supervision in the acoustic evidence. Our project page is available at https://audiorubrics.github.io.

Fangxu Yu, Tao Feng, Dehai Min +6

University of Maryland, College Park · University of Illinois Urbana-Champaign · University of Illinois Chicago +2

Audio Reasoning Rubric-Based RL Reinforcement Learning with Verifiable Rewards

Aug 3, 2026cs.LG

Qwen-CUA: Native Computer Use for (almost) Everything

Native computer use offers a general interface for agents to operate almost any software available to people, but requires long-horizon state tracking, large-scale interactive experience, and learning from sparse yet verifiable outcomes. We introduce Qwen-CUA, a native computer-use agent with a 397B-A17B Qwen mixture-of-experts backbone. It observes only screenshots and acts through keyboard and mouse events, without DOM trees, accessibility metadata, or task-specific APIs. Its scaffold maintains up to 20 active screenshots and folds older visual history in fixed-size blocks to retain recent evidence while preserving reusable prompt prefixes. For training, we build a cloud rollout fleet with access to nearly 100,000 vCPUs and tens of thousands of concurrent environments, construct approximately 40,000 verifiable tasks, and collect personalized long-horizon workflows across everyday and professional software. We optimize complete trajectories with verifiable rewards and trajectory slicing, while iterative training runs refresh supervised data and recalibrate reinforcement-learning tasks. Across eight benchmarks, Qwen-CUA outperforms Qwen3.7 and remains competitive with leading proprietary systems, reaching 86.2 on OSWorld-Verified and 18.5/48.4 binary/partial completion on OSWorld 2.0. Scaling the same recipe to a model with over one trillion parameters yields Qwen-CUA-Max, improving these scores to 87.6 and 21.2/53.3. Qwen-CUA also reduces RedTeamCUA attack success from 36.6 to 16.4 relative to Qwen3.7. Efficiency analyses, a browser deployment, and Bash-augmented experiments further characterize practical behavior. These results establish native computer use as a broadly capable agent foundation and highlight scalable verifiable interaction and hybrid tool use as key directions.

Dunjie Lu, Shuai Bai, Tianyi Bai +43

Computer-Use Agent Benchmarks Computer-Use Agents Reinforcement Learning with Verifiable Rewards LLM Agent Training Long-Horizon LLM Agents

Aug 3, 2026cs.LG

Start Classifying: Categorical Critics for LLM Reinforcement Learning

Proximal Policy Optimization (PPO) for large language models typically trains its critic by mean-squared-error (MSE) regression on scalar value targets. Although scalar MSE is statistically valid for estimating the conditional expected return, sparse binary rewards in reinforcement learning with verifiable rewards (RLVR) make critic optimization and calibration especially consequential: small value errors directly distort the scalar advantages used by PPO. We study whether a classification-based training objective can improve this critic signal. HL-Gauss PPO replaces the scalar MSE head with a categorical predictor over a discretized value support, trained by cross-entropy against smoothed HL-Gauss targets. Its output is decoded to a scalar expectation for standard GAE and PPO; the actor update is therefore unchanged and is not distributional. Across mathematical reasoning, tool-augmented math, and Search-R1, and on both Qwen2.5 and Qwen3 backbones, HL-Gauss PPO consistently improves over strong PPO and DAPO baselines. Controls with one-hot, two-hot, and Bernoulli two-bin critics show that neither a larger output head nor binary classification alone explains the gains. On a common collection of reasoning prefixes, HL-Gauss improves Brier score and calibration error and yields more symmetric, lower-variance advantages. These results position categorical value learning as an effective optimization surrogate for PPO critics in RLVR.

Zhijian Zhou, Long Li, Xuan Zhang +7

Fudan University · Shanghai Innovation Institute · Tencent YoutuLab +2

RL for Language Model Reasoning Reinforcement Learning with Verifiable Rewards Proximal Policy Optimization

Aug 3, 2026cs.AI

Deferred Exposure of Future Trajectories for Verifiable Reasoning in Autonomous Driving VLMs

Recent Vision-Language-Action (VLA) models for autonomous driving (AD) increasingly utilize chain-of-thought (CoT) supervision to enhance the reasoning capabilities of their Vision-Language Model (VLM) components, yet existing annotation pipelines commonly expose the teacher model to the logged ground-truth (GT) future trajectory. We empirically show that this induces trajectory anchoring bias: teacher models rationalize the revealed outcome rather than infer a decision from scene evidence, producing less causally faithful CoTs and substantially more severe hallucinations, especially in causally challenging scenes. Removing the GT trajectory eliminates this shortcut, but open-ended trajectory generation entangles high-level decision-making with precise geometric synthesis and low-level dynamics. To make trajectory-level driving decisions verifiable without requiring open-ended trajectory synthesis, we introduce Autonomous-Driving Multiple-Choice Question (AD-MCQ), which casts planning as selection among explicit trajectory candidates. Taking this a step further, we propose Deferred Exposure of Future Trajectories for RLVR (DEFT-RLVR) to transform future trajectories from pre-decision anchors into post-decision verification targets. Experimental results show that DEFT-RLVR improves AD reasoning while preserving or even enhancing general visual capabilities. With VLM-only inference and controllable difficulty through candidate construction, AD-MCQ provides a flexible, scalable, and extensible foundation for future research on verifiable AD reasoning.

Zixuan Huang, Yang Zhou, Kaixuan Wang +7

1Beihang University · 2Zhuoyu Technology, Shenzhen, China · 3Zhejiang University +1

VLM Reasoning Reinforcement Learning with Verifiable Rewards Autonomous Driving Planning

Aug 3, 2026cs.AI

TCPO: Turn-Level Credit Policy Optimization

Verifier-guided reinforcement learning has become a powerful paradigm for improving LLM reasoning. In multi-turn settings, models receive a verifier score after each turn and iteratively refine their outputs. Although such scores provide dense feedback, they do not directly provide dense credit: a score measures the quality of the current output, while credit should measure how the current turn changes the refinement trajectory. We propose TCPO, a turn-level credit assignment method for verifier-guided multi-turn RL. TCPO casts credit assignment as score-to-credit conversion and constructs turn-level advantages through reference-based comparisons: retrospective credit captures immediate progress and regression relative to the best prior state; hindsight delayed credit identifies non-improving turns with later payoff; and selective fixed-history counterfactual estimation refines high-surprisal turns under the same history. Experiments on math reasoning, code generation, and AppWorld agent tasks show that TCPO improves or matches the strongest baselines across model scales, task domains, and verifier types. TCPO achieves the best or tied-best best-turn Pass@8 on Qwen3-4B and DeepSeek-R1-Distill-Llama-8B, reduces turns to success, and improves multi-turn agent performance. These results highlight score-to-credit conversion as a central ingredient for verifier-guided multi-turn policy optimization.

Sicong Liao, Zhi Chen, Yaohua Tang

Moore Threads AI

RL for Language Model Reasoning Credit Assignment in RL Step-Level Credit Assignment in RL Reinforcement Learning with Verifiable Rewards Step-Level Credit Assignment RL for LLM Agents

Aug 3, 2026cs.AI

Does the Competitive Component of Adversarial Self-Play Improve Legal Reasoning? A Controlled Negative Result

Adversarial self-play is an appealing recipe for legal reasoning: have a student model draft an argument, have an adversary attack it, and reward the student when its argument survives the attack. We designed exactly such a training signal -- a verifiable "survival" reward in which both the student's cited authorities and the adversary's counter-authorities are checked by a citation verifier, so that survival is decided on verified grounds rather than rhetoric, and fabricated citations are automatically neutralized. We then asked a narrow but important question: does the competitive component itself -- the adversary and the survival reward -- add anything on top of an otherwise identical non-competitive training run? Across four independent tests -- a bootstrap comparison, a two-seed replication, a paired per-case adversarial-robustness comparison, and a blinded head-to-head judgment of generated arguments, plus a follow-up pilot with a deliberately strengthened self-play adversary -- the competitive component produced no reliable benefit. The blinded judgment gave a 49% win rate (binomial p approx. 1.000); the strengthened-adversary pilot gave a 50% win rate (32:32, p approx. 1.000). An early apparent +29% advantage reversed and proved to be a small-sample artifact. We report this as an honest negative result. The value of the paper is reproducibility and the sharing of concrete pitfalls: an initially promising metric that inverted on more data, and an adversarial-robustness metric that silently collapsed to plain recall once the adversary stopped citing the same authorities as the gold answer. This null is consistent with, and reconfirms in the legal domain, the conclusion of the companion coding-domain study (Kim, 2026, arXiv:2607.08255) that the value of multi-teacher curricula arises from constructing a verifiable environment rather than from competition itself.

Miseog Shawn Kim

Preprint, 2026-08-02

Adversarial Robustness Reinforcement Learning with Verifiable Rewards Legal Reasoning

Aug 2, 2026cs.CL

EviSD: Evidence-Conditioned Self-Distillation for Search-Augmented Agents

Outcome-based reinforcement learning enables search-augmented language agents to learn from verifiable final answers, but its trajectory-level credit cannot distinguish the contributions of individual actions in a multi-turn search process. We propose EviSD, an evidence-conditioned self-distillation framework that uses instance-level supporting evidence as privileged information for search actions and golden answers as complementary privilege for answer actions. During training, the student samples actions from the original context, while the same model re-scores them as a privileged teacher under an action-aligned context. EviSD converts the detached teacher--student gap into a bounded correction to the outcome-derived GRPO advantage and applies it only to generated action spans. This design localizes privileged guidance while preserving the update direction determined by the outcome reward, without an auxiliary distillation objective or any change at inference time. Across seven question-answering benchmarks and three backbones spanning model scales and generations, EviSD achieves the highest macro-average Exact Match in all evaluated settings, outperforming the strongest compared methods by 1.3--2.3 points while modulating only 6.7%--15.1% of response tokens. Code is available at https://github.com/JiananXie/EviSD.

Jianan Xie, Xin Sun, Zhongqi Chen +4

ShanghaiTech University · NLPR, MAIS, CASIA · Ant Group

Agentic Search Credit Assignment in RL Reinforcement Learning with Verifiable Rewards Self-Distillation RL for LLM Agents

Aug 1, 2026cs.CL

Distill Where You Fail: Recovering Learning Signals of Negative RL-Groups from Adaptive Teacher Guidance

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for post-training large language models (LLMs). While Group Relative Policy Optimization (GRPO) is widely adopted, it suffers from sparse reward signals and loses gradients entirely when all responses within a group receive identical rewards. On-policy distillation (OPD) offers a natural remedy by providing dense, token-level supervision from a teacher model. However, naively combining GRPO with OPD leads to degraded performance, due to three underlying causes: not all samples benefit from distillation; fitting too quickly to the teacher undermines the exploratory capacity of RL; and OPD's advantages are asymmetric, suppressing most tokens. To address these challenges, we propose RSTG (Recovering Learning Signals via Adaptive Teacher Guidance), which applies distillation selectively and precisely where it matters most. At the sample level, OPD is restricted to negative zero-variance prompts with each sample weighted by the teacher's confidence score. At the token level, distillation targets only tokens with high student entropy or large teacher-student divergence. We further augment training with SFT on correct trajectories generated by the teacher model, injecting positive gradient signals where RL yields none. Experiments demonstrate that RSTG substantially outperforms naive GRPO+OPD by +4.02% on math and +3.05% on code.

Zhuowen Han, Jinwei Xiao, Zhengxi Lu +9

TJUNLP Lab, School of Computer Science and Technology, Tianjin University · Meituan Longcat Team

Self-Training for Language Models RL for Language Model Reasoning Selective Knowledge Distillation Reinforcement Learning with Verifiable Rewards On-Policy Distillation Knowledge Distillation