A Comparative Theoretical Analysis of Entropy Control Methods in Reinforcement Learning
Provides theoretical guidelines for entropy control in LLM posttraining, addressing premature convergence in RL-based reasoning enhancement.
The paper theoretically compares entropy regularization and covariance-based entropy control in RL for LLMs, showing that covariance-based methods achieve asymptotic unbiasedness while traditional regularization introduces bias leading to suboptimal policies.
Reinforcement learning (RL) has become a key approach for enhancing reasoning in large language models (LLMs), yet scalable training is often hindered by the rapid collapse of policy entropy, which leads to premature convergence and performance saturation. This paper provides a comparative theoretical analysis of two entropy control strategies: traditional entropy regularization and the recently proposed covariance-based mechanism. We establish a unified framework for entropy dynamics under softmax parameterization, showing that entropy change is governed by the covariance between log-probabilities and logit updates. Our analysis reveals that traditional entropy regularization introduces a dense, persistent bias that modifies the stationary condition, leading to suboptimal policies, while covariance-based methods selectively regularize a sparse subset of high-covariance tokens and achieve asymptotic unbiasedness when the regularization coefficient is annealed. These results provide principled guidelines for entropy control in LLM posttraining, with implications for scaling RL to larger models and more complex reasoning tasks.