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

📅 2025-06-03
📈 Citations: 0
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🤖 AI Summary
This paper addresses the pervasive “zero-reward assumption” challenge in LLM reinforcement learning—namely, the difficulty of obtaining token-level immediate rewards, leaving only sparse, response-level rewards. We introduce the Trajectory Policy Gradient Theorem, which rigorously proves for the first time that response-level rewards can yield unbiased estimates of the true token-level policy gradient. Methodologically, we establish a mathematical equivalence between response-level rewards and token-level gradients, revealing that mainstream algorithms—including PPO and GRPO—are inherently compatible with this setting. Leveraging this insight, we propose TRePO, a lightweight, memory-efficient algorithm. Key contributions include: (1) providing a unified theoretical foundation for response-level RL; (2) substantially reducing reward engineering overhead in LLM alignment; and (3) achieving competitive performance with simplified implementation and improved training efficiency.

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📝 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.
Problem

Research questions and friction points this paper is trying to address.

Addresses Zero-Reward Assumption in LLM reinforcement learning
Proves response-level rewards suffice for unbiased policy gradients
Introduces Token-Reinforced Policy Optimization for efficient fine-tuning
Innovation

Methods, ideas, or system contributions that make the work stand out.

Trajectory Policy Gradient Theorem for unbiased estimation
Response-level reward model simplifies token-level rewards
Token-Reinforced Policy Optimization (TRePO) for efficiency
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