RL for Language Model Reasoning

With respect to improving the reasoning accuracy of LLMs, the representative reinforcement learning (RL) method - Group Relative Policy Optimization (GRPO) - has achieved critical success, yet it still suffers from the issue of insignificant reward signals. This paper introduces ReST-RL, a unified Reinforced Self-Training (ReST) policy-value framework that reconnects policy optimization and value-guided search to improve LLM reasoning ability. Firstly, ReST-GRPO adopts an optimized ReST-style algorithm to reshape the policy-induced trajectory distribution by increasing the reward variance of GRPO sampling and exposing the policy to more informative partial states, thereby improving training efficiency and effectiveness. Then, we further introduce a decoding optimization method, VM-MCTS, which trains a Value Model (VM) from self-collected Monte-Carlo Tree Search (MCTS) targets and deploys it through an adapted MCTS algorithm to provide precise process signals and verification scores, further enhancing reasoning accuracy. These two stages are internally dependent - ReST-GRPO yields higher-quality trajectories for value learning with VM-MCTS, which in turn enables more effective inference-time search. We validate our framework on multiple coding benchmarks (e.g., APPS, BigCodeBench, and HumanEval), where it significantly outperforms other reinforcement training baselines (naive GRPO, DAPO, and ReST-DPO), as well as decoding and verification baselines (e.g., PRM-BoN and ORM-MCTS), indicating its power to strengthen LLM reasoning capability. Moreover, we further evaluate ReST-RL on out-of-domain math and science reasoning tasks, where it achieves improved performance without target-domain tuning and favorable end-to-end efficiency trade-offs, providing preliminary transfer evidence beyond our primary coding domain.

Advanced reasoning in LLMs on challenging domains like mathematical reasoning can be tackled using verifiable rewards based reinforced fine-tuning (ReFT). In standard ReFT frameworks, a behavior model generates multiple completions with answers per problem, for the answer to be then scored by a reward function. While such RL post-training methods demonstrate significant performance improvements across challenging reasoning domains, the computational cost of generating completions during training with multiple inference steps makes the training cost non-trivial. To address this, we draw inspiration from off-policy RL, and speculative decoding to introduce a novel ReFT framework, dubbed Nested-ReFT, where a subset of layers of the target model acts as the behavior model to generate off-policy completions during training. The behavior model configured with dynamic layer skipping per batch during training decreases the inference cost compared to the standard ReFT frameworks. Our theoretical analysis shows that Nested-ReFT yields unbiased gradient estimates with controlled variance. Our empirical analysis demonstrates improved computational efficiency measured as tokens/sec across multiple math reasoning benchmarks and model sizes. Additionally, we explore three variants of bias mitigation to minimize the off-policyness in the gradient updates that allows for maintaining performance that matches the baseline ReFT performance.

Large Reasoning Models (LRMs) can exhibit step-by-step reasoning, reflection, and backtracking, but these behaviors are often unregulated, leading to overthinking. As a result, LRMs continue generating redundant reasoning even after reaching high-confidence conclusions. This increases inference cost and latency, limiting practical deployment. The root cause is the absence of an intrinsic mechanism to monitor the reasoning state and decide when to continue, backtrack, or stop. We propose MERA, a meta-cognitive reasoning framework that decouples reasoning from control to enable independent optimization of control strategies. MERA constructs high-quality reasoning-control supervision data via a takeover-based pipeline, and transforms long-horizon traces into structured reasoning-control alternating sequences for training. The model is trained with supervised fine-tuning to internalize the structured separation, and further optimized with Control-Segment Policy Optimization (CSPO), which combines segment-wise GRPO with control masking to focus learning on control segments. Experiments across reasoning benchmarks show that MERA improves both efficiency and accuracy.

Large reasoning models (LRMs) often exhibit overthinking, producing verbose Chain-of-Thought (CoT) traces that increase inference cost and obscure the underlying reasoning process. Existing CoT compression methods mainly rely on global length rewards, which conflate necessary intermediate reasoning with redundant text and may therefore compromise reasoning fidelity. This paper revisits overthinking from a semantic-efficiency perspective and decomposes CoT redundancy into two distinct forms: internal redundancy, defined as informational stagnation before the first correct answer, and external redundancy, defined as superfluous continuation after the first correct answer. Based on this decomposition, we propose a dual-penalty reinforcement learning framework that separately optimizes reasoning progress and termination behavior. Specifically, a sliding-window semantic similarity metric penalizes low-progress reasoning segments, while a normalized external-redundancy metric discourages post-answer continuation. Experiments on GSM8K, MATH500, and AIME24 across different model scales show that our method reduces average reasoning length by 41.3% on the 1.5B model and 40.1% on the 7B model, while preserving competitive accuracy and achieving the best overall accuracy-efficiency score among evaluated baselines. The learned compression behavior further transfers to out-of-domain reasoning tasks, including GPQA and LiveCodeBench. More importantly, our analysis reveals a clear asymmetry between the two redundancy types: external redundancy can be largely removed with little performance loss, whereas internal redundancy compression follows a sensitive accuracy-efficiency trade-off. These results suggest that effective CoT compression should optimize semantic efficiency rather than sequence length alone, offering a principled route toward more concise, efficient, and interpretable LRMs.

The proliferation of Large Language Models (LLMs) in medicine has enabled impressive capabilities, yet a critical gap remains in their ability to perform systematic, transparent, and verifiable reasoning, a cornerstone of clinical practice. This has catalyzed a shift from single-step answer generation to the development of LLMs explicitly designed for medical reasoning. This paper provides the first systematic review of this emerging field. We propose a taxonomy of reasoning enhancement techniques, categorized into training-time strategies (e.g., supervised fine-tuning, reinforcement learning) and test-time mechanisms (e.g., prompt engineering, multi-agent systems). We analyze how these techniques are applied across different data modalities (text, image, code) and in key clinical applications such as diagnosis, education, and treatment planning. Furthermore, we survey the evolution of evaluation benchmarks from simple accuracy metrics to sophisticated assessments of reasoning quality and visual interpretability. Based on an analysis of 60 seminal studies from 2022-2025, we conclude by identifying critical challenges, including the faithfulness-plausibility gap and the need for native multimodal reasoning, and outlining future directions toward building efficient, robust, and sociotechnically responsible medical AI.

Large Language Models (LLMs) often produce plausible but poorly-calibrated answers, limiting their reliability on reasoning-intensive tasks. Recent research suggests that Chain-of-Thought (CoT) reasoning paths are inherent in pre-trained LLMs and can be elicited by simply altering the decoding process, where the presence of a CoT path correlates with higher answer confidence. Building on these insights, we present Reinforcement Learning from Self-Feedback (RLSF), a post-training stage that utilises the model's intrinsic confidence as a self-generated reward. By generating multiple CoT decoding beams from a frozen LLM, we compute the confidence of each final answer span and rank the resulting traces accordingly to create synthetic preferences. These preferences are subsequently utilised to fine-tune the policy through standard preference optimisation, requiring no human labels, gold answers, or externally curated rewards. RLSF simultaneously (i) refines the model's probability estimates--restoring well-behaved calibration--and (ii) strengthens step-by-step reasoning, yielding improved performance on arithmetic reasoning and multiple-choice question answering. By converting a model's own uncertainty into structured self-feedback, RLSF affirms reinforcement learning on intrinsic model behaviour as a principled and data-efficient component of the LLM post-training pipeline. Our results demonstrate that leveraging these inherent reasoning capabilities provides a robust path for enhancing model reliability without manual prompt engineering or external supervision.

Existing informal language-based (e.g., human language) Large Language Models (LLMs) trained with Reinforcement Learning (RL) face a significant challenge: their verification processes, which provide crucial training signals, are neither reliable nor scalable. In fact, the prevalent large proprietary models could hardly generate verifiable programs. A promising yet largely uncharted alternative is formal language-based reasoning. Grounding LLMs in rigorous formal systems where generative models operate in formal language spaces (e.g., Dafny) enables the automatic and mathematically provable verification of their reasoning processes and outcomes. This capability is pivotal for achieving large-scale, reliable formal software verification. It is a common practice to employ human-annotated chain-of-thought and answers to induce the reasoning and coding capabilities of LLMs. Unfortunately, it becomes unacceptably all-consuming to provide such priors for supervising complex programming tasks. In this work, we systematically explore ways to reduce human annotations with the formal language, Dafny, as the main environment for our pilot study. Our pipeline mainly relies on introducing an automatic and scalable data curation pipeline, and careful RL designs integrated with feedback from the formal language verifier. We introduce DafnyComp, a benchmark of compositional formal programs with auto-formalized specifications for specification reasoning. Our supervised fine-tuning (SFT) stage enables even small models (e.g., 0.5B) to generate syntactically valid and verifiable Dafny code, surpassing proprietary models. RL with regularization further improves performance, achieving stronger generalization to out-of-domain tasks and outperforming all strong baselines on the challenging DafnyComp benchmark.

Next-word prediction (NWP) trains language models against a single observed continuation, even though many contexts admit multiple plausible next words. Recent RL-based next-word reasoning methods make this tension explicit: they reward a model for producing a rationale that supports one context-conditioned continuation, which can turn a pre-existing preference into a confident, self-justifying trajectory. We introduce BOW, an RL framework that instead trains models to produce self-contained, neutral, and comprehensive descriptions of the plausible next-word space. The policy generates a next-word reasoning trajectory from the full context, but a frozen scorer computes the core reward from that trajectory alone, without separately receiving the context. BOW-Reg adds a lightweight breadth regularizer to this core reward to discourage premature collapse. On two model backbones, BOW remains competitive with the original models and often outperforms trained baselines across ten general reasoning benchmarks. On benchmarks testing ambiguous references and word meanings, BOW-Reg achieves the highest SharedRef correctness and the lowest HoWN-Simple single-sense collapse on both backbones. Human evaluation further shows that BOW-Reg produces broader next-word reasoning trajectories, while direct next-word-prediction evaluation shows that these trajectories remain predictive.

Natural Language Inference (NLI) is a central task in natural language understanding with applications in fact-checking, question answering, and information retrieval. Despite its importance, current NLI systems heavily rely on supervised learning with datasets that often contain annotation artifacts and biases, limiting generalization and real-world applicability. In this work, we apply a reinforcement learning-based approach using Group Relative Policy Optimization (GRPO) for Chain-of-Thought (CoT) learning in NLI, eliminating the need for human-labeled rationales and enabling this type of training on challenging datasets such as ANLI. We fine-tune 7B, 14B, and 32B language models using parameter-efficient techniques (LoRA and QLoRA), demonstrating strong performance across standard and adversarial NLI benchmarks. At the 32B scale, GRPO-trained models generalize better than other supervised baselines in adversarial sets. With AWQ quantization, the 32B model fits within 22GB of CUDA memory. This work provides a scalable and practical framework for building robust NLI systems without sacrificing inference quality.

Reinforcement finetuning (RFT) has shown great potential for enhancing the mathematical reasoning capabilities of large language models (LLMs), but it is often sample- and compute-inefficient, requiring extensive training. In this work, we introduce AdaRFT (Adaptive Curriculum Reinforcement Finetuning), a method that significantly improves the efficiency of RFT through adaptive curriculum learning. AdaRFT dynamically adjusts the difficulty of training problems based on the model's recent reward signals, ensuring that the model consistently trains on tasks that are challenging but solvable. This adaptive sampling strategy accelerates learning by maintaining an optimal difficulty range, avoiding wasted computation on problems that are too easy or too hard. AdaRFT requires only a lightweight extension to standard RFT algorithms like Proximal Policy Optimization (PPO), without modifying the reward function or model architecture. Experiments on competition-level math datasets demonstrate that AdaRFT improves convergence efficiency and reasoning performance. Given problem-level difficulty annotations, AdaRFT reduces RFT training time by up to 2 times across data distributions and model scales, offering a more scalable and effective RFT framework.

Natural Language to SQL (NL2SQL) aims to translate natural language queries into executable SQL statements, offering non-expert users intuitive access to databases. While recent approaches leveraging large-scale private LLMs such as GPT-4 have achieved state-of-the-art results, they face two critical challenges: the lack of openness and reproducibility, and the prohibitive computational cost of test-time scaling. To address these issues, we explore improving the model-level performance of small-scale public LLMs in NL2SQL under resource-constrained settings. Our exploratory experiments reveal the potential of task decomposition for enhancing NL2SQL performance, but also highlight the difficulty of enabling LLMs to decompose queries effectively. Motivated by these findings, we propose LearNAT, a novel framework designed to enhance decomposition capabilities of LLM. LearNAT introduces (1) a Decomposition Synthesis Procedure, which leverages AST-guided search with pruning strategies to generate verifiable and efficient decompositions, and (2) Margin-Aware Reinforcement Learning, which provides fine-grained preference optimization for multi-step reasoning beyond standard DPO. Extensive experiments on benchmark datasets demonstrate that LearNAT significantly improves the performance of small-scale LLMs, achieving results comparable to GPT-4 with only a 7B parameter model. These results validate the effectiveness of verifiable decomposition and fine-grained preference learning in advancing NL2SQL towards openness, transparency, and efficiency. Our code is publicly available at https://github.com/MrBlankness/LearNAT.

The reasoning abilities of large language models (LLMs) have improved with chain-of-thought (CoT) prompting, allowing models to solve complex tasks stepwise. However, training CoT capabilities requires detailed reasoning data, which is often scarce. The self-taught reasoner (STaR) framework addresses this by using reinforcement learning to automatically generate reasoning steps, reducing reliance on human-labeled data. Although STaR and its variants have demonstrated empirical success, a theoretical foundation explaining these improvements is lacking. This work provides a theoretical framework for understanding the effectiveness of reinforcement learning on CoT reasoning and STaR. Our contributions are: (1) criteria for the quality of pre-trained models necessary to initiate effective reasoning improvement; (2) an analysis of policy improvement, showing why LLM reasoning improves iteratively with STaR; (3) conditions for convergence to an optimal reasoning policy; and (4) an examination of STaR's robustness, explaining how it can improve reasoning even when incorporating occasional incorrect steps. We also run RL-STaR on GPT-2, Qwen2.5-0.5B and Phi-3-mini, and the measured return curves follow the ones the analysis predicts. This framework bridges empirical findings with theoretical insights, advancing reinforcement learning approaches for reasoning in LLMs.

Autoregressive large language models (LLMs) compress knowledge from their training data through next-token conditional distributions. This limits tractable querying of this knowledge to start-to-end autoregressive sampling. However, many tasks of interest -- including sequence continuation, infilling, and other forms of constrained generation -- involve sampling from intractable posterior distributions. We address this limitation by using amortized Bayesian inference to sample from these intractable posteriors. Such amortization is algorithmically achieved by fine-tuning LLMs via diversity-seeking reinforcement learning algorithms: generative flow networks (GFlowNets). We empirically demonstrate that this distribution-matching paradigm of LLM fine-tuning can serve as an effective alternative to maximum-likelihood training and reward-maximizing policy optimization. As an important application, we interpret chain-of-thought reasoning as a latent variable modeling problem and demonstrate that our approach enables data-efficient adaptation of LLMs to tasks that require multi-step rationalization and tool use.

Reward hacking is a form of misalignment in which models overoptimize proxy rewards without genuinely solving the underlying task. Precisely measuring reward hacking occurrence remains challenging because true task rewards are often expensive or impossible to compute. We introduce Countdown-Code, a minimal environment where models can both solve a mathematical reasoning task and manipulate the test harness. This dual-access design creates a clean separation between proxy rewards (test pass/fail) and true rewards (mathematical correctness), enabling accurate measurement of reward-hacking rates. Using this environment, we study reward hacking in open-weight LLMs and find that such behaviors can be unintentionally learned during supervised fine-tuning (SFT) when even a small fraction of reward-hacking trajectories leak into training data. As little as 1% contamination in distillation SFT data is sufficient for models to internalize reward hacking which resurfaces during subsequent reinforcement learning (RL). We further show that RL amplifies misalignment and drives its generalization beyond the original domain. We open-source our environment and code to facilitate future research on reward hacking in LLMs. Our results reveal a previously underexplored pathway through which reward hacking can emerge and persist in LLMs, underscoring the need for more rigorous validation of synthetic SFT data. Code is available at https://github.com/zohaib-khan5040/Countdown-Code.

Existing approaches to post-train models for long-context tasks face complementary limitations: (i) supervised fine-tuning (SFT) provides stable supervision but suffers from exposure bias; (ii) reinforcement learning methods such as Group Relative Policy Optimization (GRPO) train on model-generated trajectories but struggle with long-horizon credit assignment and sparse rewards; and (iii) on-policy distillation (OPD) provides dense token-level guidance but does not directly optimize task rewards. We study these complementary strategies for long-context alignment and derive a recipe that combines GRPO with OPD-style teacher guidance: the student learns from its own rollouts using outcome-level rewards, while a stronger teacher provides dense token-level regularization in place of the standard reference policy. This is especially useful when process-level supervision is difficult to obtain. To support this study, we introduce LongBlocks, a synthetic multilingual dataset spanning multi-hop reasoning, contextual grounding, and long-form generation. Through controlled ablations, we isolate the roles of cold-start initialization, teacher anchoring, and data mixing, showing that our recipe yields a more stable and effective path to long-context reasoning than GRPO or OPD while preserving short-context capabilities.

We introduce a novel method that averages the logits of a frozen reference policy (e.g., SFT) and a trainable policy, and incorporate the method into Group Relative Policy Optimization (GRPO). In contrast to Reinforcement Learning with Verifiable Rewards (RLVR) methods, our proposal does not involve a Kullback Leibler (KL) regularization or critic; the trainable policy and the reference anchor are coupled through the logit averaging structure to leverage the reasoning expertise of the trainable policy while maintaining the formatting advantage of SFT. Our method is evaluated on MATH, cn-k12, and MMLU, and the results show a higher accuracy or at least comparable accuracy relative to the canonical KL-regularized GRPO.

Classical reinforcement learning (RL) typically seeks a deterministic policy that maximizes the expected sum of a scalar reward. Yet, modern applications such as language model fine-tuning or scientific discovery demand diversity. Existing remedies such as entropy regularization or diversity bonuses often require fragile trade-offs that sacrifice performance for stochasticity or rely on heuristic metrics that can misalign policy rankings. We argue that diversity is more naturally understood as the rational response to uncertainty in the reward. When the reward function is not perfectly known--as is the case with ambiguous preferences or imperfect reward models--committing to a single action can be sub-optimal. Building on this, we propose a fundamental reformulation of the RL objective by replacing the scalar reward with a distribution over reward functions, and applying a non-linear objective over sets of actions. The result is a framework in which calibrated behavioural diversity emerges naturally, remains controllable through the reward function distribution, and is obtained without sacrificing expected reward. Focusing on the contextual bandit setting as commonly used in large language model (LLM) post-training, we derive a principled gradient estimator for this objective and prove that our formulation naturally generalizes both vanilla policy gradient and more recently developed action-set approaches. We provide didactic experiments which complement our theoretical results, and our large-scale empirical results in LLM reasoning further demonstrate that this framework offers a robust and theoretically grounded alternative for complex RL tasks where the traditional formulation of the problem fails to induce the desired breadth of agent behaviour.