The Energy Loss Phenomenon in RLHF: A New Perspective on Mitigating Reward Hacking

This work identifies the Energy Loss Phenomenon in Reinforcement Learning from Human Feedback (RLHF) and its connection to reward hacking. Specifically, energy loss in the final layer of a Large Language Model (LLM) gradually increases during the RL process, with an excessive increase in energy loss characterizing reward hacking. Beyond empirical analysis, we further provide a theoretical foundation by proving that, under mild conditions, the increased energy loss reduces the upper bound of contextual relevance in LLMs, which is a critical aspect of reward hacking as the reduced contextual relevance typically indicates overfitting to reward model-favored patterns in RL. To address this issue, we propose an Energy loss-aware PPO algorithm (EPPO) which penalizes the increase in energy loss in the LLM's final layer during reward calculation to prevent excessive energy loss, thereby mitigating reward hacking. We theoretically show that EPPO can be conceptually interpreted as an entropy-regularized RL algorithm, which provides deeper insights into its effectiveness. Extensive experiments across various LLMs and tasks demonstrate the commonality of the energy loss phenomenon, as well as the effectiveness of \texttt{EPPO} in mitigating reward hacking and improving RLHF performance.