# MCPO: Mastery-Consolidated Policy Optimization for Large Reasoning Models

arXiv: https://arxiv.org/abs/2604.16972 · HTML: https://mlsanity.com/paper/2604.16972/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 28 of its 36 references that are in the map.
- First posted on arXiv 18 Apr 2026.

## Placed in

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

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Group Sequence Policy Optimization](https://mlsanity.com/paper/2507.18071/) (2025)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [GLM-5: from Vibe Coding to Agentic Engineering](https://mlsanity.com/paper/2602.15763/) (2026)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [Kimi K2.5: Visual Agentic Intelligence](https://mlsanity.com/paper/2602.02276/) (2026)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Pass@k Training for Adaptively Balancing Exploration and Exploitation of Large Reasoning Models](https://mlsanity.com/paper/2508.10751/) (2025)
- [Act Only When It Pays: Efficient Reinforcement Learning for LLM Reasoning via Selective Rollouts](https://mlsanity.com/paper/2506.02177/) (2025)
- [Beyond Pass@1: Self-Play with Variational Problem Synthesis Sustains RLVR](https://mlsanity.com/paper/2508.14029/) (2025)
- [No Prompt Left Behind: Exploiting Zero-Variance Prompts in LLM Reinforcement Learning via Entropy-Guided Advantage Shaping](https://mlsanity.com/paper/2509.21880/) (2025)
- [DCPO: Dynamic Clipping Policy Optimization](https://mlsanity.com/paper/2509.02333/) (2025)
- [NGRPO: Negative-enhanced Group Relative Policy Optimization](https://mlsanity.com/paper/2509.18851/) (2025)
- [ODE Analysis of Stochastic Gradient Methods with Optimism and Anchoring for Minimax Problems](https://mlsanity.com/paper/1905.10899/) (2019)
- [DisCO: Reinforcing Large Reasoning Models with Discriminative Constrained Optimization](https://mlsanity.com/paper/2505.12366/) (2025)
- [Quantile Advantage Estimation: Stabilizing RLVR for LLM Reasoning](https://mlsanity.com/paper/2509.22611/) (2025)
- [SAPO: Self-Adaptive Process Optimization Makes Small Reasoners Stronger](https://mlsanity.com/paper/2601.20312/) (2026)

## Built on by (most cited first, 1 of 1)

- [Learning to Solve, Forgetting to Retain: Correct-Set Turnover in RLVR](https://mlsanity.com/paper/2606.03087/) (2026)

## Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising approach to improve the reasoning abilities of Large Language Models (LLMs). Among RLVR algorithms, Group Relative Policy Optimization (GRPO) and its variants have demonstrated strong performance and high training efficiency. However, GRPO-style objectives exhibit two issues on high accuracy prompts including mastered prompts (rollout accuracy =1) and majority-correct prompts (rollout accuracy in (0.5,1)). For mastered prompts, group-relative advantages vanish, yielding no training signal and unconstrained policy drift that can cause forgetting. For majority-correct prompts, the induced query weight shrinks as accuracy increases, weakening consolidation from partial correctness to mastery. To alleviate this, we propose Mastery-Consolidated Policy Optimization (MCPO), which introduces (i) a hinge-KL regularizer applied exclusively to mastered prompts to bound harmful policy drift between successive gradient steps, and (ii) a weighting mechanism that prioritizes majority-correct prompts to better allocate optimization effort. Extensive experiments across three mathematical benchmarks demonstrate that MCPO consistently improves pass@1 performance. Counter-intuitively, rather than restricting exploration, MCPO boosts pass@k metrics, indicating that mastery consolidation further catalyzes solution diversity.