# CE-GPPO: Coordinating Entropy via Gradient-Preserving Clipping Policy Optimization in Reinforcement Learning

arXiv: https://arxiv.org/abs/2509.20712 · HTML: https://mlsanity.com/paper/2509.20712/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 12 of its 16 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## 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, 12 of 12)

- [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)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [Reasoning with Exploration: An Entropy Perspective](https://mlsanity.com/paper/2506.14758/) (2025)
- [Understanding the impact of entropy on policy optimization](https://mlsanity.com/paper/1811.11214/) (2018)
- [AceReason-Nemotron: Advancing Math and Code Reasoning through Reinforcement Learning](https://mlsanity.com/paper/2505.16400/) (2025)
- [Klear-Reasoner: Advancing Reasoning Capability via Gradient-Preserving Clipping Policy Optimization](https://mlsanity.com/paper/2508.07629/) (2025)

## Built on by (most cited first, 23 of 23)

- [Step-GUI Technical Report](https://mlsanity.com/paper/2512.15431/) (2025)
- [When Importance Sampling Misallocates Credit: Asymmetric Ratios for Outcome-Supervised RL](https://mlsanity.com/paper/2510.06062/) (2025)
- [Revisiting Entropy in Reinforcement Learning for Large Reasoning Models](https://mlsanity.com/paper/2511.05993/) (2025)
- [On-policy Distillation with Verifiable Reward](https://mlsanity.com/paper/2608.24696/) (2026)
- [EntroPIC: Towards Stable Long-Term Training of LLMs via Entropy Stabilization with Proportional-Integral Control](https://mlsanity.com/paper/2511.15248/) (2025)
- [SCOPE-RL: Stable and Quantitative Control of Policy Entropy in RL Post-Training](https://mlsanity.com/paper/2510.08141/) (2025)
- [MASPO: Unifying Gradient Utilization, Probability Mass, and Signal Reliability for Robust and Sample-Efficient LLM Reasoning](https://mlsanity.com/paper/2602.17550/) (2026)
- [AT2PO: Agentic Turn-based Policy Optimization via Tree Search](https://mlsanity.com/paper/2601.04767/) (2026)
- [Credit Where It is Due: Cross-Modality Connectivity Drives Precise Reinforcement Learning for MLLM Reasoning](https://mlsanity.com/paper/2602.11455/) (2026)
- [From log π to π: Taming Divergence in Soft Clipping via Bilateral Decoupled Decay of Probability Gradient Weight](https://mlsanity.com/paper/2603.14389/) (2026)
- [GoLongRL: Capability-Oriented Long Context Reinforcement Learning with Multitask Alignment](https://mlsanity.com/paper/2605.19577/) (2026)
- [Flexible Entropy Control in RLVR with a Gradient-Preserving Perspective](https://mlsanity.com/paper/2602.09782/) (2026)
- [QUATRO: Query-Adaptive Trust Region Policy Optimization for LLM Fine-tuning](https://mlsanity.com/paper/2602.04620/) (2026)
- [Targeted Exploration via Unified Entropy Control for Reinforcement Learning](https://mlsanity.com/paper/2604.14646/) (2026)
- [Entropy Polarity in Reinforcement Fine-Tuning: Direction, Asymmetry, and Control](https://mlsanity.com/paper/2605.11775/) (2026)
- [STARE: Surprisal-Guided Token-Level Advantage Reweighting for Policy Entropy Stability](https://mlsanity.com/paper/2606.19236/) (2026)
- [Entropy Ratio Clipping as a Soft Global Constraint for Stable Reinforcement Learning](https://mlsanity.com/paper/2512.05591/) (2025)
- [The Role of Entropy in Visual Grounding: Analysis and Optimization](https://mlsanity.com/paper/2512.06726/) (2025)
- [ACRL: Adaptive Control of Training-Inference Discrepancy for Stable Reinforcement Learning](https://mlsanity.com/paper/2607.24062/) (2026)
- [Soft Sequence Policy Optimization](https://mlsanity.com/paper/2602.19327/) (2026)
- [Smooth Gate Functions for Soft Advantage Policy Optimization](https://mlsanity.com/paper/2602.19345/) (2026)
- [Entropy Pacing Policy Optimization for Multi-Task Agentic Reinforcement Learning](https://mlsanity.com/paper/2607.07178/) (2026)
- [A Closed-Loop Non-Asymptotic Convergence Analysis of PPO with Learned Critics and Clipping](https://mlsanity.com/paper/2610.10273/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) has become a powerful paradigm for optimizing large language models (LLMs) to handle complex reasoning tasks. A core challenge in this process lies in managing policy entropy, which reflects the balance between exploration and exploitation during training. Existing methods, such as proximal policy optimization (PPO) and its variants, discard valuable gradient signals from low-probability tokens due to the clipping mechanism. We systematically analyze the entropy dynamics and reveal that these clipped tokens play a critical yet overlooked role in regulating entropy evolution. We propose Coordinating Entropy via Gradient-Preserving Policy Optimization (CE-GPPO), a novel algorithm that reintroduces gradients from clipped tokens in native PPO in a gentle and bounded manner. By controlling the magnitude of gradients from tokens outside the clipping interval, CE-GPPO is able to achieve an exploration-exploitation trade-off. We provide theoretical justification and empirical evidence showing that CE-GPPO effectively mitigates entropy instability. Extensive experiments on mathematical reasoning benchmarks show that CE-GPPO consistently outperforms strong baselines across different model scales.