# ERPO: Token-Level Entropy-Regulated Policy Optimization for Large Reasoning Models

arXiv: https://arxiv.org/abs/2603.28204 · HTML: https://mlsanity.com/paper/2603.28204/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 30 Mar 2026.

## Placed in

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

## Builds on (most cited first, 17 of 17)

- [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)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Geometric-Mean Policy Optimization](https://mlsanity.com/paper/2507.20673/) (2025)
- [TreePO: Bridging the Gap of Policy Optimization and Efficacy and Inference Efficiency with Heuristic Tree-based Modeling](https://mlsanity.com/paper/2508.17445/) (2025)
- [BAPO: Stabilizing Off-Policy Reinforcement Learning for LLMs via Balanced Policy Optimization with Adaptive Clipping](https://mlsanity.com/paper/2510.18927/) (2025)
- [Rethinking Entropy Regularization in Large Reasoning Models](https://mlsanity.com/paper/2509.25133/) (2025)
- [Attention Illuminates LLM Reasoning: The Preplan-and-Anchor Rhythm Enables Fine-Grained Policy Optimization](https://mlsanity.com/paper/2510.13554/) (2025)
- [Seer: Online Context Learning for Fast Synchronous LLM Reinforcement Learning](https://mlsanity.com/paper/2511.14617/) (2025)
- [Learning to Optimize Multi-Objective Alignment Through Dynamic Reward Weighting](https://mlsanity.com/paper/2509.11452/) (2025)
- [Knapsack RL: Unlocking Exploration of LLMs via Optimizing Budget Allocation](https://mlsanity.com/paper/2509.25849/) (2025)
- [Plan Then Action:High-Level Planning Guidance Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2510.01833/) (2025)
- [EEPO: Exploration-Enhanced Policy Optimization via Sample-Then-Forget](https://mlsanity.com/paper/2510.05837/) (2025)
- [MAPO: Mixed Advantage Policy Optimization](https://mlsanity.com/paper/2509.18849/) (2025)
- [Let it Calm: Exploratory Annealed Decoding for Verifiable Reinforcement Learning](https://mlsanity.com/paper/2510.05251/) (2025)

## Built on by (most cited first, 6 of 6)

- [Where Rollouts Begin: Low-Load, High-Leverage First-Token Diversification for RLVR](https://mlsanity.com/paper/2605.28295/) (2026)
- [When Implausible Tokens Get Reinforced: Tail-Aware Credit Calibration for LLM Reinforcement Learning](https://mlsanity.com/paper/2607.07976/) (2026)
- [Holder Policy Optimisation](https://mlsanity.com/paper/2605.12058/) (2026)
- [Momentum for Reasoning: Dense Intrinsic Signals in Policy Optimization](https://mlsanity.com/paper/2606.08815/) (2026)
- [Advancing Entropy-Level Credit Assignment in RLVR via Proximal Entropy Policy Optimization](https://mlsanity.com/paper/2609.39402/) (2026)
- [GRPODropout: Less is More for Online Reinforcement Learning Rollouts](https://mlsanity.com/paper/2610.11854/) (2026)

## Abstract (arXiv)

Reinforcement learning from verifiable rewards has significantly advanced the reasoning capabilities of large language models. However, Group Relative Policy Optimization (GRPO) typically assigns a uniform, sequence-level advantage to all tokens, thereby overlooking the intrinsic information heterogeneity along reasoning chains. We show that this coarse-grained credit assignment leads to premature entropy collapse and encourages the model to generate redundant, low-quality reasoning paths. Through systematic empirical analysis, we identify Critical Decision Pivots (CDPs): transient high-entropy states where the policy's trajectory is most sensitive to perturbations. These pivots represent the "forks in the road" where effective multi-path exploration is most crucial yet often suppressed by uniform advantage signals. Building on these insights, we propose Entropy-Regulated Policy Optimization (ERPO), which transitions the optimization focus from coarse sequences to fine-grained token dynamics. ERPO introduces three synergistic components: (i) Entropy-aware Gating, which adaptively amplifies exploration at CDPs to facilitate diverse path discovery; (ii) Bucket-based Implicit Normalization, which mitigates difficulty bias by aligning token progress windows; and (iii) Result-anchored Advantage Synthesis, which re-weights token-level signals via outcome-driven anchors. Extensive experiments on competitive mathematical benchmarks demonstrate that ERPO significantly outperforms GRPO. Notably, ERPO not only boosts reasoning accuracy but also yields significantly more concise and robust derivation paths, while achieving performance comparable to large models with orders of magnitude more parameters.