{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/trajectory-bellman-residual-minimization-a","title":"Trajectory Bellman Residual Minimization: A Simple Value-Based Method for LLM Reasoning","arxiv_id":"2505.15311","date":"2025-05-21","proceeding":null,"authors":["Yurun Yuan","Fan Chen","Zeyu Jia","Alexander Rakhlin","Tengyang Xie"],"abstract":"Policy-based methods currently dominate reinforcement learning (RL) pipelines for large language model (LLM) reasoning, leaving value-based approaches largely unexplored. We revisit the classical paradigm of Bellman Residual Minimization and introduce Trajectory Bellman Residual Minimization (TBRM), an algorithm that naturally adapts this idea to LLMs, yielding a simple yet effective off-policy algorithm that optimizes a single trajectory-level Bellman objective using the model's own logits as $Q$-values. TBRM removes the need for critics, importance-sampling ratios, or clipping, and operates with only one rollout per prompt. We prove convergence to the near-optimal KL-regularized policy from arbitrary off-policy data via an improved change-of-trajectory-measure analysis. Experiments on standard mathematical-reasoning benchmarks show that TBRM consistently outperforms policy-based baselines, like PPO and GRPO, with comparable or lower computational and memory overhead. Our results indicate that value-based RL might be a principled and efficient alternative for enhancing reasoning capabilities in LLMs.","url_abs":"https://arxiv.org/abs/2505.15311v1","url_pdf":"https://arxiv.org/pdf/2505.15311v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[],"tasks":[{"task_slug":"language-modeling","task_name":"Language Modeling"},{"task_slug":"language-modelling","task_name":"Language Modelling"},{"task_slug":"large-language-model","task_name":"Large Language Model"},{"task_slug":"mathematical-reasoning","task_name":"Mathematical Reasoning"},{"task_slug":"reinforcement-learning-1","task_name":"Reinforcement Learning (RL)"}],"methods":[{"method_slug":"entropy-regularization","method_name":"Entropy Regularization"},{"method_slug":"ppo","method_name":"PPO"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2505.15311","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2505.15311"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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