# Entropy-Preserving Reinforcement Learning

arXiv: https://arxiv.org/abs/2603.11682 · HTML: https://mlsanity.com/paper/2603.11682/

## 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 43 of its 56 references that are in the map.
- First posted on arXiv 12 Mar 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)
- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 30 of 43)

- [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)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?](https://mlsanity.com/paper/2504.13837/) (2025)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [AppWorld: A Controllable World of Apps and People for Benchmarking Interactive Coding Agents](https://mlsanity.com/paper/2407.18901/) (2024)
- [Cognitive Behaviors that Enable Self-Improving Reasoners, or, Four Habits of Highly Effective STaRs](https://mlsanity.com/paper/2503.01307/) (2025)
- [DD-PPO: Learning Near-Perfect PointGoal Navigators from 2.5 Billion Frames](https://mlsanity.com/paper/1911.00357/) (2019)
- [Reinforcement Learning for Reasoning in Large Language Models with One Training Example](https://mlsanity.com/paper/2504.20571/) (2025)
- [TTRL: Test-Time Reinforcement Learning](https://mlsanity.com/paper/2504.16084/) (2025)
- [Spurious Rewards: Rethinking Training Signals in RLVR](https://mlsanity.com/paper/2506.10947/) (2025)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [Maximum Entropy RL (Provably) Solves Some Robust RL Problems](https://mlsanity.com/paper/2103.06257/) (2021)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [RL with KL penalties is better viewed as Bayesian inference](https://mlsanity.com/paper/2205.11275/) (2022)

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

- [On-policy Distillation with Verifiable Reward](https://mlsanity.com/paper/2608.24696/) (2026)
- [A Tale of Two Temperatures: Simple, Efficient, and Diverse Sampling from Diffusion Language Models](https://mlsanity.com/paper/2604.09921/) (2026)
- [AEM: Adaptive Entropy Modulation for Multi-Turn Agentic Reinforcement Learning](https://mlsanity.com/paper/2605.00425/) (2026)
- [Entropy Polarity in Reinforcement Fine-Tuning: Direction, Asymmetry, and Control](https://mlsanity.com/paper/2605.11775/) (2026)
- [Addressing Performance Saturation for LLM RL via Precise Entropy Curve Control](https://mlsanity.com/paper/2604.26326/) (2026)
- [Reinforcement Learning over Predictive Distributions for LLM Regression](https://mlsanity.com/paper/2605.20740/) (2026)
- [Multi-Step Likelihood-Ratio Correction for Reinforcement Learning with Verifiable Rewards](https://mlsanity.com/paper/2605.20865/) (2026)
- [Understanding Evolution Strategies for LLM Reasoning: Broader Reasoning Coverage than GRPO](https://mlsanity.com/paper/2608.27351/) (2026)
- [Headroom-Drift Replay: A Primitive for Principled Replay Control in GRPO](https://mlsanity.com/paper/2609.03941/) (2026)
- [Dependency-Aware Reward Shaping for Agentic Reinforcement Learning](https://mlsanity.com/paper/2610.01207/) (2026)
- [Exploration-Preserving Policy Optimization](https://mlsanity.com/paper/2610.04011/) (2026)

## Abstract (arXiv)

Policy gradient algorithms have driven many recent advancements in language model reasoning. An appealing property is their ability to learn from exploration on their own trajectories, a process crucial for fostering diverse and creative solutions. As we show in this paper, many policy gradient algorithms naturally reduce the entropy -- and thus the diversity of explored trajectories -- as part of training, yielding a policy increasingly limited in its ability to explore. In this paper, we argue that entropy should be actively monitored and controlled throughout training. We formally analyze the contributions of leading policy gradient objectives on entropy dynamics, identify empirical factors (such as numerical precision) that significantly impact entropy behavior, and propose explicit mechanisms for entropy control. These include REPO, a family of algorithms that modify the advantage function to regulate entropy, and ADAPO, an adaptive asymmetric clipping approach. Models trained with our entropy-preserving methods maintain diversity throughout training, yielding final policies that are more performant and retain their trainability for sequential learning in new environments.