mlsanityData to 7 Oct 2026

A Comparative Theoretical Analysis of Entropy Control Methods in Reinforcement Learning

arXiv 2604.09676 ↗First posted 2 Apr 2026cs.LG cs.AIcited by 0

On the map: LLM reasoning → Reinforcement learning for reasoning

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning. Builds on 15 of its 35 references that are in the map. First posted on arXiv 2 Apr 2026.

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15 of 35 references.

Closest ancestors · 5

Same direction, newest first

  1. 2025The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models28 May
  2. 2025Understanding R1-Zero-Like Training: A Critical Perspective26 Mar
  3. 2025DAPO: An Open-Source LLM Reinforcement Learning System at Scale18 Mar
  4. 2025Process Reinforcement through Implicit Rewards3 Feb
  5. 2017Proximal Policy Optimization Algorithms20 Jul

Other references · 10

  1. 2022Training language models to follow instructions with human feedbackcited by 15,712
  2. 2023Llama 2: Open Foundation and Fine-Tuned Chat Modelscited by 12,865
  3. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 8,851
  4. 2020Scaling Laws for Neural Language Modelscited by 6,411
  5. 2018Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actorcited by 4,635
  6. 2017Deep reinforcement learning from human preferencescited by 3,846
  7. 2022Training Compute-Optimal Large Language Modelscited by 2,927
  8. 2015Trust Region Policy Optimizationcited by 2,503
  9. 2016Optimization Methods for Large-Scale Machine Learningcited by 1,140
  10. 2022Scaling Laws for Reward Model Overoptimizationcited by 1,056

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  3. 2025Rethinking Entropy Interventions in RLVR: An Entropy Change Perspective
  4. 2025Revisiting Entropy in Reinforcement Learning for Large Reasoning Models
  5. 2026Addressing Performance Saturation for LLM RL via Precise Entropy Curve Control
  6. 2026On the Entropy Dynamics in Reinforcement Fine-Tuning of Large Language Models
  7. 2026Asymmetric Advantage Modulation Calibrates Entropy Dynamics in RLVR
  8. 2026Flexible Entropy Control in RLVR with a Gradient-Preserving Perspective