RL-based post-training for reasoning models is increasingly bottlenecked by repeated fresh rollout generation, particularly in agentic settings where environment interaction dominates wall-clock cost. Replay can reduce this burden by reusing past trajectories, but existing methods typically embed it within larger training pipelines involving exploration, experience restructuring, or mixed-policy optimization. This makes replay's own contribution difficult to isolate. We ask a focused question: how far can principled replay selection alone go? We introduce Headroom-Drift Replay, a group-level replay control primitive for GRPO that separates reuse into two decisions. Headroom ranks stored groups by remaining learning value, while Drift gates them by compatibility with the current policy. The fresh on-policy stream remains unchanged, and the method adds no auxiliary generation or training machinery. Across mathematical reasoning, multimodal reasoning, and Agentic Search benchmarks, this single intervention outperforms naive replay and matches or exceeds broader replay methods on Avg Mean@32. In Agentic Search, where environment interaction dominates cost, it delivers comparable quality at materially lower wall-clock time.
Gijs Kassenaar, Zhao Yang, Vincent François-Lavetcs.AI
Reasoning language models trained with reinforcement learning typically operate under a fixed token budget rather than an explicitly adaptive one, which can lead to over-computation on easy problems and insufficient computation on difficult ones. We study whether a model can learn to allocate its own reasoning effort by choosing, as the first token of its response, one of three modes: \textsc{NoThink} (answer as quickly as possible), \textsc{Short} (brief reasoning), or \textsc{Long} (extended reasoning). The choice is learned inside Group Relative Policy Optimization (GRPO) with no separate router, through a shaped reward that makes each mode worthwhile at a different response length, together with hard per-mode token caps that keep the modes distinct. On a 1.5B distilled model trained on MATH, the three modes emerge without collapsing to a single choice, and the brief modes end up more accurate than \textsc{Long}, which shows that the router sorts problems by difficulty rather than at random. Averaged over three seeds, the resulting policy stays close to the base model's accuracy on the held-out MATH500 ($0.782$ vs.\ $0.796$) while cutting the mean response length from $4{,}796$ to $2{,}811$ tokens (a $41\%$ reduction). Interestingly, it also transfers to other benchmarks without retraining, with the largest savings where problems are easier, with for instance 76\% token reduction on GSM8K and at higher accuracy than the baselines at similar response length. In short, we build a reasoning model that adaptively chooses how much to reason for each problem.
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
Recent large reasoning models often develop long chain-of-thought responses during reinforcement learning (RL), resulting in high inference latency and deployment cost. Existing methods for response length control typically rely on explicit length penalties or additional control modules, which require careful tuning and may compromise reasoning quality. We propose Quadrant-weighted Sampling for Length-aware Policy Optimization (QLPO), a simple resampling-based variant of GRPO that introduces implicit length control without modifying the reward function. QLPO first over-generates candidate responses and then resamples the training group by preserving the empirical correct/incorrect ratio while favoring short correct responses and long incorrect responses. This reshapes the training distribution and implicitly encourages shorter model outputs. Across models ranging from 1.5B to 32B parameters, including both base models and strong reasoning models, QLPO consistently improves the accuracy-length trade-off. It reduces response length by 30% to 70% while preserving reasoning performance. These results suggest that structured resampling provides an effective and robust approach to efficient reasoning.
Reinforcement learning from verifiable rewards (e.g. GRPO) is the engine behind today's reasoning models, yet it grades only the final answer. On hard problems this trains models to write more rather than to think better, since the trace itself is never graded and no label for good thinking exists. We introduce Agon, which makes two competing models each other's graders. Both attempt the same problem; in alternating roles, one drafts a solution and the other reads it while solving, and each is rewarded for out-solving the other. To win, a model must out-reason a rival that has seen its work, so reasoning is judged implicitly during training, with no process labels and no reward model. Because both models are optimized, each faces a progressively stronger rival, which single-model RL cannot provide. The two need only be comparably strong and behaviorally different. At inference the pair deploys as it trains, a two-stage cascade in which one model drafts and the other answers after reading the draft. On the hard split of DeepMath with Qwen3, this doubles GRPO's pass@1, roughly eight times the gain of an untrained Mixture-of-Agents pass over the same base. The ordering replicates on competitive-programming code and across model families (Qwen3.5, Gemma 4). For now the models talk in text; the next step is to let them reason together in latent space.
Reasoning language models frequently overthink: generating extended chains of behaviors such as hedging, approach abandonment, and self contradiction that consume tokens without improving answers. We show that these behaviors are not merely a consequence of length; even when controlling for response length, incorrect traces exhibit higher rates of unproductive self-reflection than correct ones. Addressing this requires identifying where self-reflection helps vs hurts, but obtaining these step-level annotations is costly. We observe that intermediate answer commitments within reasoning traces can provide a cheap proxy: by comparing each final answer candidate in the trace to the ground truth, we can determine whether subsequent reflection is productive without any additional supervision. Building on this insight, we propose DASH (Drift Aware advantage SHaping), which assigns segment-level credit based on whether each reasoning segment leads toward or away from correctness. On competition-level math benchmarks, DASH achieves the highest accuracy where overthinking is prevalent (AIME25: 50.8% vs. 45.4% GRPO) while reducing overthinking behaviors and achieving more productive self-correction than baselines.
Jungseob Lee, Seungyoon Lee, Seongtae Hong +3cs.AI cs.CL
Training large language models to reason efficiently is a critical challenge. While integrating length-penalizing rewards into Group Relative Policy Optimization (GRPO) aims to reduce verbosity, it frequently triggers reward collapse, severely degrading reasoning capabilities. Through a systematic evaluation of various reward configurations, we identify the root mechanism: GRPO's group normalization creates divergent advantages when incorrect answers receive continuous length penalties. Consequently, methods penalizing the length of incorrect answers are structurally prone to collapse under sustained optimization. Furthermore, restricting penalties exclusively to correct answers avoids this primary failure, but leaves the model susceptible to a stochastic collapse driven by response over-compression. To robustly prevent both failure modes, we propose ACOER (Adaptive Correct-Only Efficiency Reward). ACOER eliminates the structural penalty loop by isolating brevity bonuses to correct completions and prevents stochastic compression via dynamic budget normalization and control-loop penalty adjustments. Evaluated across diverse mathematical reasoning benchmarks, ACOER improves overall accuracy compared to the base model while reducing token generation by over 60%, establishing a fundamentally stable approach for efficiency-aware optimization.
Reinforcement Learning with Verifiable Rewards (RLVR) has become a standard paradigm for enhancing the capability of large reasoning models. RLVR typically samples responses independently and optimizes the policy using from final answers. This paradigm has two limitations. First, independently responses often contain similar intermediate reasoning steps, causing redundant exploration and wasted computation. Second, sparse final-answer rewards make it hard to identify useful steps. Tree-based methods partly address this problem by sharing prefixes and comparing branches from the same prefix to provide fine-grained signals. However, tree branches are still expanded independently. When different branches reach similar reasoning states, they cannot share information and repeat similar exploration. Moreover, tree-based methods ignore such dispersion and only perform local comparisons within separate branches, which can lead to higher variance in advantage estimation. To address this challenge, we propose GraphPO (Graph-based Policy Optimization), a novel RL framework that represents rollouts as a directed acyclic graph, with reasoning steps as edges and semantic states summarized from the reasoning paths as nodes. GraphPO merges semantically equivalent reasoning paths into equivalence classes, allowing them to share suffixes and reallocating budget away from redundant expansions to diverse exploration. Furthermore, we assign efficiency advantages to incoming edges and correctness advantages to outgoing edges, thereby improving inference efficiency while deriving process supervision from outcome. Theory shows that GraphPO reduces advantage-estimation variance and enhances reasoning efficiency. Experiments on three LLMs across reasoning and agentic search benchmarks show that GraphPO consistently outperforms chain- and tree-based baselines with the same token budgets or response budgets.
Long-form chain-of-thought reasoning can improve LLM performance on complex tasks, but models often continue generating unnecessary reasoning after a correct answer has emerged. We refer to this behavior as overthinking. We study this phenomenon from the perspective of GRPO-style reinforcement learning (RL) post-training, framing it as a training-time credit-assignment problem rather than merely a decoding-time stopping problem. In rollouts sampled at the onset of GRPO training, we observe that successful trajectories can exhibit a slightly higher degree of overthinking than unsuccessful trajectories for the same prompts. This early imbalance provides a starting point for an undesirable feedback loop: because GRPO assigns sequence-level credit, it cannot distinguish the solution-reaching prefix from the unnecessary continuation that lengthens a successful trajectory. Both receive positive update signal, allowing the initial imbalance to grow into more severe overthinking during training. To address this issue, we introduce Dynamic Rollout Editing (DRE), a training-time intervention for successful trajectories that continue thinking after answer emergence. DRE preserves the accepted verified prefix, edits the remaining thinking, and prefers the edited trajectory within the same RL group, weakening the preference signal for unnecessary thinking without penalizing the reasoning needed to reach the answer. Experiments across diverse tasks show the effectiveness of DRE.
On-policy self-distillation (OPSD) provides dense, token-level supervision for reasoning models by aligning a model's own distribution with the distribution it produces under privileged context, typically a verified solution. However, we show that the learning signal drawn from this distributional gap concentrates on style tokens rather than task-bearing ones, as the hinted model tends to produce more direct, shorter outputs. We term this pathology \emph{privilege-induced style drift}, which destabilizes training or causes response length to shrink. To address this, we propose \textbf{RLCSD} (Reinforcement Learning with Contrastive on-policy Self-Distillation), which mitigates this drift by contrasting the teacher-student gap under a correct hint against that under a wrong hint, suppressing the style shift that conditioning on a hint tends to induce regardless of correctness, and yielding a signal that is more concentrated on task-bearing tokens. Experiments on Qwen3 (1.7B/4B/8B) and Olmo-3-7B-Think across mathematical and logical reasoning show that RLCSD consistently outperforms GRPO and prior OPSD methods. We further show that the contrastive principle is general: it plugs into existing OPSD methods to improve them, and its underlying insight extends to the broader cross-model on-policy distillation setting.
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.
Rishabh Agrawal, Jacob Fein-Ashley, Paria Rashidinejadcs.LG cs.AI cs.CL
Reasoning models have advanced rapidly, but the dominant reinforcement learning from verifiable rewards (RLVR) recipe remains surprisingly narrow: sample many responses and reward each with a single bit indicating whether the final answer is correct. Yet many settings provide rich feedback, including execution traces, tool outputs, expert corrections, and model self-evaluations. We study how to use such feedback through a distributional variant of the classic imitation learning algorithm DAgger, where the learner has local access to an expert distribution on states visited by the current policy. This yields a simple forward cross-entropy objective that admits a blackbox expert and whose sequence-level gradient {conduct rich credit assignment by propagating} future expert-student disagreement back to earlier decisions. We show that prior RL with self-distillation objectives based on reverse KL or Jensen-Shannon fail to guarantee monotonic policy improvement: even when the expert has higher reward, their updates may increase probability on worse actions. In contrast, we show that forward cross-entropy admits monotonic policy improvement and enjoys guarantees on regret. We further show that our objective optimizes a lower bound on teacher-weighted likelihood of success, leading to improved Pass@N. Empirically, our approach, DistIL, improves over RLVR and RL with self-distillation baselines across a variety of domains: scientific reasoning, coding, and solving hard mathematical problems.
Guangcheng Zhu, Shenzhi Yang, Haobo Wang +7cs.LG cs.AI
Reinforcement learning with verifiable rewards (RLVR) has greatly advanced large reasoning models (LRMs), but it requires timely training on a huge fully-annotated dataset. To this end, data-efficient RLVR methods have been widely studied from two perspectives: (i) data selection methods identify a small subset of "golden" samples that yield near-full-data performance, but they rely on a pre-existing pool of labeled data. (ii) unsupervised RLVR methods train the model using its own internal supervision signals on large-scale unlabeled data, yet they exhibit suboptimal performance. Accordingly, we investigate the "pick in the dark" setup for RLVR, which aims to select, without prior supervision, unlabeled samples that are most beneficial for training and worthy of annotation. Through systematic analysis, we demonstrate that smart picks hinge on a well-calibrated uncertainty estimator to enable strategic partitioning of data for adaptive training regimes. Building on this insight, we propose PivotTrace, a three-way data triage framework that leverages attention dynamics to trace metacognitive pivots during reasoning. By precisely quantifying uncertainty through pivot density, PivotTrace achieves automated data routing to synergistically maximize both annotation and training efficiency. Empirically, PivotTrace surpasses the fully supervised LRM with only 29.3% annotated samples and 2.75 faster convergence.
Recent advances in language models have established reinforcement learning as the primary paradigm for eliciting self-correction and long-chain reasoning. While group relative policy optimization (GRPO) offers superior scalability by eliminating the critic network, deploying it on a central infrastructure entails collecting a large volume of data from distributed owners, which poses significant privacy risks. To address these concerns, we introduce federated GRPO (FGRPO), a framework designed to decentralize the fine-tuning of reasoning models across heterogeneous data owners. To effectively mitigate the instability caused by divergent reward scales across heterogeneous tasks, FGRPO incorporates an adaptive aggregation mechanism based on relative performance gain. By characterizing each client's improvement relative to its personalized historical baseline, the framework dynamically prioritizes effective learning trajectories regardless of local task difficulty. FGRPO ensures robust convergence on non-IID data while preserving data privacy.
Reinforcement learning with verifiable rewards (RLVR) has become an effective paradigm for improving reasoning language models on tasks such as mathematics, coding, and scientific question answering. However, widely used group-relative objectives, such as GRPO, summarize each sampled group with scalar statistics and therefore discard fine-grained relational information among candidate responses. This weakens credit assignment under sparse outcome rewards, especially when multiple generated solutions differ only subtly in reasoning quality. We propose \textbf{LamPO}, a \textbf{Lambda-Style Policy Optimization} method that replaces scalar group advantages with a \emph{Pairwise Decomposed Advantage}. LamPO aggregates pairwise reward gaps within each response group and modulates each comparison by a confidence-aware weight computed from sequence log-probability differences, while retaining the critic-free and clipped-update structure of PPO-style optimization. When reference solutions are available, we further add a lightweight ROUGE-L-based dense auxiliary reward to reduce reward sparsity. Experiments on AIME24, AIME25, MATH-500, and GPQA-Diamond with Qwen3-1.7B, Qwen3-4B, and Phi-4-mini show that LamPO consistently improves over GRPO and recent RLVR variants, with more stable training dynamics and better sample efficiency.
Adapting reasoning models to new tasks during post-training with only output-level supervision stalls under reinforcement learning from verifiable rewards (RLVR) when the initial success probability $p_0$ is small. Using the Tsallis $q$-logarithm, we define a loss family $J_Q$ that interpolates between RLVR (at $q{=}0$, the exploitation pole) and the log-marginal-likelihood over latent trajectories (at $q{=}1$, the density-estimation pole). All members share the same per-example gradient direction, differing only by a scalar amplification $P_{θ^{-q}}$ that reweights each instance independently of the learning rate. This amplification is the mechanism that addresses cold-start stalling: under gradient flow, the exploitation pole requires $Ω(\frac{1}{p_0})$ time to escape cold start, while the density-estimation pole escapes in $Θ\big(\log(\frac{1}{p_0})\big)$; intermediate $q$ trades escape speed against noise memorization. Because $P_θ$ is intractable, we derive two Monte Carlo estimators from the two factorizations of the gradient: Gradient-Amplified RL (GARL) samples from the prior and amplifies the RL gradient, and Posterior-Attenuated Fine-Tuning (PAFT) importance-resamples from the posterior and runs standard SFT. Both have bias $O\big(\frac{q}{M P_θ^{q+1}}\big)$; GARL has lower variance, PAFT has semantically coherent gradients. On FinQA, HotPotQA, and MuSiQue, GARL at $q{=}0.75$ substantially mitigates cold-start stalling, escaping cold start where GRPO fails entirely. In warm start, GARL at low $q$ dominates FinQA where training is stable; on HotPotQA and MuSiQue, GARL destabilizes during training, and PAFT at $q{=}0.75$ provides stable gradients (best overall on HotPotQA at 47.9 maj@16, $+14.4$ over GRPO).