# Revisiting Entropy Regularization: Adaptive Coefficient Unlocks Its Potential for LLM Reinforcement Learning

arXiv: https://arxiv.org/abs/2510.10959 · HTML: https://mlsanity.com/paper/2510.10959/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 30 of its 50 references that are in the map.
- First posted on arXiv 13 Oct 2025.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 30 of 30)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [Exploration by Random Network Distillation](https://mlsanity.com/paper/1810.12894/) (2018)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [RLAIF vs. RLHF: Scaling Reinforcement Learning from Human Feedback with AI Feedback](https://mlsanity.com/paper/2309.00267/) (2023)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [SimpleRL-Zoo: Investigating and Taming Zero Reinforcement Learning for Open Base Models in the Wild](https://mlsanity.com/paper/2503.18892/) (2025)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [Provably Efficient Exploration in Policy Optimization](https://mlsanity.com/paper/1912.05830/) (2019)
- [RIDE: Rewarding Impact-Driven Exploration for Procedurally-Generated Environments](https://mlsanity.com/paper/2002.12292/) (2020)
- [Outcome-based Exploration for LLM Reasoning](https://mlsanity.com/paper/2509.06941/) (2025)
- [An Empirical Study on Eliciting and Improving R1-like Reasoning Models](https://mlsanity.com/paper/2503.04548/) (2025)
- [Randomized Exploration for Reinforcement Learning with General Value Function Approximation](https://mlsanity.com/paper/2106.07841/) (2021)
- [QuestA: Expanding Reasoning Capacity in LLMs via Question Augmentation](https://mlsanity.com/paper/2507.13266/) (2025)
- [RL Tango: Reinforcing Generator and Verifier Together for Language Reasoning](https://mlsanity.com/paper/2505.15034/) (2025)
- [Navigate the Unknown: Enhancing LLM Reasoning with Intrinsic Motivation Guided Exploration](https://mlsanity.com/paper/2505.17621/) (2025)
- [CDE: Curiosity-Driven Exploration for Efficient Reinforcement Learning in Large Language Models](https://mlsanity.com/paper/2509.09675/) (2025)
- [PAG: Multi-Turn Reinforced LLM Self-Correction with Policy as Generative Verifier](https://mlsanity.com/paper/2506.10406/) (2025)
- [When to Continue Thinking: Adaptive Thinking Mode Switching for Efficient Reasoning](https://mlsanity.com/paper/2505.15400/) (2025)
- [CURE: Critical-Token-Guided Re-Concatenation for Entropy-Collapse Prevention](https://mlsanity.com/paper/2508.11016/) (2025)
- [Staying in the Sweet Spot: Responsive Reasoning Evolution via Capability-Adaptive Hint Scaffolding](https://mlsanity.com/paper/2509.06923/) (2025)
- [Know When to Explore: Difficulty-Aware Certainty as a Guide for LLM Reinforcement Learning](https://mlsanity.com/paper/2509.00125/) (2025)
- [Reasoner for Real-World Event Detection: Scaling Reinforcement Learning via Adaptive Perplexity-Aware Sampling Strategy](https://mlsanity.com/paper/2507.01327/) (2025)

## Built on by (most cited first, 11 of 11)

- [Where to Spend Rollouts: Hit-Utility Optimal Rollout Allocation for Group-Based RLVR](https://mlsanity.com/paper/2605.07114/) (2026)
- [Tracking Drift: Variation-Aware Entropy Scheduling for Non-Stationary Reinforcement Learning](https://mlsanity.com/paper/2601.19624/) (2026)
- [Nudging Beyond the Comfort Zone: Efficient Strategy-Guided Exploration for RLVR](https://mlsanity.com/paper/2605.15726/) (2026)
- [When Does Multi-Agent Collaboration Help? An Entropy Perspective](https://mlsanity.com/paper/2602.04234/) (2026)
- [Offline Exploration-Aware Fine-Tuning for Long-Chain Mathematical Reasoning](https://mlsanity.com/paper/2603.16206/) (2026)
- [PAEC: Position-Aware Entropy Calibration for LLM Reasoning in RLVR](https://mlsanity.com/paper/2606.08543/) (2026)
- [Beyond Entropy: Learning from Token-Level Distributional Deviations for LLM Reasoning](https://mlsanity.com/paper/2606.19771/) (2026)
- [Influence-Directed Distillation: Solving the Diversity Bottleneck in Sampled-Token On-Policy Distillation](https://mlsanity.com/paper/2608.29846/) (2026)
- [CurveRL: Principled Distribution-Aware Context Reweighting for LLM Reasoning](https://mlsanity.com/paper/2605.24331/) (2026)
- [Diversity Over Frequency: Rethinking Tool Use in Visual Chain-of-Thought Agents](https://mlsanity.com/paper/2606.00096/) (2026)
- [Exploration-Preserving Policy Optimization](https://mlsanity.com/paper/2610.04011/) (2026)

## Abstract (arXiv)

Reasoning ability has become a defining capability of Large Language Models (LLMs), with Reinforcement Learning with Verifiable Rewards (RLVR) emerging as a key paradigm to enhance it. However, RLVR training often suffers from policy entropy collapse, where the policy becomes overly deterministic, hindering exploration and limiting reasoning performance. While entropy regularization is a common remedy, its effectiveness is highly sensitive to the fixed coefficient, making it unstable across tasks and models. In this work, we revisit entropy regularization in RLVR and argue that its potential has been largely underestimated. Our analysis shows that (i) tasks of varying difficulty demand distinct exploration intensities, and (ii) balanced exploration may require the policy entropy to be maintained within a moderate range below its initial level. Therefore, we propose Adaptive Entropy Regularization (AER)--a framework that dynamically balances exploration and exploitation via three components: difficulty-aware coefficient allocation, initial-anchored target entropy, and dynamic global coefficient adjustment. Experiments on multiple mathematical reasoning benchmarks show that AER consistently outperforms baselines, improving both reasoning accuracy and exploration capability.