Response-Level Rewards Are All You Need for Online Reinforcement Learning in LLMs: A Mathematical Perspective

• URL: http://arxiv.org/abs/2506.02553v1
• Date: Tue, 03 Jun 2025 07:44:31 GMT
• Title: Response-Level Rewards Are All You Need for Online Reinforcement Learning in LLMs: A Mathematical Perspective
• Authors: Shenghua He, Tian Xia, Xuan Zhou, Hui Wei,
• Abstract summary: We study the Zero-Reward Assumption in reinforcement learning for large language models (LLMs)<n>We show that the policy gradient based on true, unknown token-level rewards can be unbiasedly estimated using only a response-level reward model.<n>We propose a new algorithm: Token-Reinforced Policy Optimization (TRePO)
• Score: 6.069069082518759
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study a common challenge in reinforcement learning for large language models (LLMs): the Zero-Reward Assumption, where non-terminal actions (i.e., intermediate token generations) receive zero task-specific immediate reward, while only the final token receives a reward for the entire response. This assumption arises frequently in practice, as precise token-level rewards are often difficult or infeasible to obtain in LLM applications. In this work, we provide a unifying theoretical perspective. We introduce the Trajectory Policy Gradient Theorem, which shows that the policy gradient based on true, unknown token-level rewards can be unbiasedly estimated using only a response-level reward model, regardless of whether the Zero-Reward Assumption holds or not, for algorithms in the REINFORCE and Actor-Critic families. This result reveals that widely used methods such as PPO, GRPO, ReMax, and RLOO inherently possess the capacity to model token-level reward signals, offering a theoretical justification for response-level reward approaches. Our findings pave the way for more practical, efficient LLM fine-tuning, allowing developers to treat training algorithms as black boxes and focus on improving the response-level reward model with auxiliary sub-models. We also offer a detailed analysis of popular RL and non-RL methods, comparing their theoretical foundations and practical advantages across common LLM tasks. Finally, we propose a new algorithm: Token-Reinforced Policy Optimization (TRePO), a theoretically grounded method that is simpler than PPO, matches GRPO in memory efficiency, and holds promise for broad applicability.

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