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Main Authors: Lei, Ming, Baehr, Christophe
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2604.09676
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author Lei, Ming
Baehr, Christophe
author_facet Lei, Ming
Baehr, Christophe
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2604_09676
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A Comparative Theoretical Analysis of Entropy Control Methods in Reinforcement Learning
Lei, Ming
Baehr, Christophe
Machine Learning
Artificial Intelligence
94-02
F.2.2
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.
title A Comparative Theoretical Analysis of Entropy Control Methods in Reinforcement Learning
topic Machine Learning
Artificial Intelligence
94-02
F.2.2
url https://arxiv.org/abs/2604.09676