Trajectory Bellman Residual Minimization: A Simple Value-Based Method for LLM Reasoning

• URL: http://arxiv.org/abs/2505.15311v1
• Date: Wed, 21 May 2025 09:41:53 GMT
• Title: Trajectory Bellman Residual Minimization: A Simple Value-Based Method for LLM Reasoning
• Authors: Yurun Yuan, Fan Chen, Zeyu Jia, Alexander Rakhlin, Tengyang Xie,
• Abstract summary: Policy-based methods currently dominate reinforcement learning pipelines for large language model (LLM) reasoning.<n>We introduce Trajectory Bellman Residual Minimization (TBRM), an algorithm that naturally adapts this idea to LLMs.<n>We prove convergence to the near-optimal KL-regularized policy from arbitrary off-policy via an improved change-of-trajectory-measure analysis.
• Score: 55.33984461046492
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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