# ACPO: Asymmetric Credit Policy Optimization via Mode-Local Entropy Surrogate

arXiv: https://arxiv.org/abs/2607.03126 · HTML: https://mlsanity.com/paper/2607.03126/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 15 of its 27 references that are in the map.
- First posted on arXiv 3 Jul 2026.

## Placed in

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

## Builds on (most cited first, 15 of 15)

- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [Rethinking Entropy Interventions in RLVR: An Entropy Change Perspective](https://mlsanity.com/paper/2510.10150/) (2025)
- [BAPO: Stabilizing Off-Policy Reinforcement Learning for LLMs via Balanced Policy Optimization with Adaptive Clipping](https://mlsanity.com/paper/2510.18927/) (2025)
- [HumanEval Pro and MBPP Pro: Evaluating Large Language Models on Self-invoking Code Generation](https://mlsanity.com/paper/2412.21199/) (2024)
- [Low-probability Tokens Sustain Exploration in Reinforcement Learning with Verifiable Reward](https://mlsanity.com/paper/2510.03222/) (2025)
- [GTPO: Stabilizing Group Relative Policy Optimization via Gradient and Entropy Control](https://mlsanity.com/paper/2508.03772/) (2025)

## Abstract (arXiv)

Outcome-supervised reinforcement learning scales to verifiable reasoning tasks, but trajectory-level rewards assign the same outcome signal to all sampled tokens, overlooking their unequal contributions to the reasoning process. Entropy provides a natural indicator of the model's decision state, yet using it for token-level credit assignment presents two key challenges: long-tail probabilities in large vocabularies corrupt both entropy values and gradients, and uncertainty carries distinct semantics across positive- and non-positive-advantage trajectories. We propose Asymmetric Credit Policy Optimization (ACPO), which replaces global entropy with the complement of the top-token probability as a mode-local proxy. Guided by gradient analysis, ACPO incorporates mismatch routing and saturation correction to shape policy updates into the desired asymmetric form, emphasizing uncertain decisions on positive trajectories while penalizing confident regions on failed ones. Theoretically, ACPO locally preserves the advantage direction while bounding surrogate error. Experiments on mathematical and coding reasoning benchmarks, including AIME 2025 and HumanEval Pro, show that ACPO consistently outperforms both entropy-aware methods (e.g., 80/20, GTPO) and strong outcome-supervised RL baselines (e.g., DAPO, SAPO).