# MDP-GRPO: Stabilized Group Relative Policy Optimization for Multi-Constraint Instruction Following

arXiv: https://arxiv.org/abs/2606.06058 · HTML: https://mlsanity.com/paper/2606.06058/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 10 of its 29 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Placed in

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

## Builds on (most cited first, 10 of 10)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [Flexible and Efficient Grammar-Constrained Decoding](https://mlsanity.com/paper/2502.05111/) (2025)
- [NGRPO: Negative-enhanced Group Relative Policy Optimization](https://mlsanity.com/paper/2509.18851/) (2025)
- [Learning Safety Constraints for Large Language Models](https://mlsanity.com/paper/2505.24445/) (2025)
- [MAPO: Mixed Advantage Policy Optimization](https://mlsanity.com/paper/2509.18849/) (2025)
- [Shaping Sparse Rewards in Reinforcement Learning: A Semi-supervised Approach](https://mlsanity.com/paper/2501.19128/) (2025)

## Built on by (most cited first, 2 of 2)

- [Advantage Scale Calibration Imbalance in Group-Relative Optimization under Low-Variance Rewards: Diagnosis and Bounded Recovery](https://mlsanity.com/paper/2609.19164/) (2026)
- [Many Right Answers, One Training Example: Removing Responder Noise from GRPO for LLM Recommenders](https://mlsanity.com/paper/2610.17771/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards is ideal for multi-constraint instruction following, yet standard group-relative policy optimization (GRPO) becomes unstable under discrete, low-dispersion rewards, where within-group reward distributions are frequently homogeneous. We identify and formalize three pathologies of z-score group normalization in this regime: low-variance amplification, mean-centering blindness, and zero-variance collapse. To address them, we propose MDP-GRPO, which stabilizes learning through (1) multi-temperature sampling to increase reward dispersion, (2) dual-anchor advantages to restore gradients in homogeneous groups and stop mean-centering blindness, (3) prospect-theoretic shaping to bound updates and penalize violations based on Kahneman and Tversky's theory, and (4) asymmetric KL regularization. Evaluated on FollowBench, IFEval, and a curated multi-constraint dataset, MDP-GRPO outperforms standard GRPO, improving strict constraint satisfaction by up to 5.0% on Llama-3.2-3B. Our method also enables stable convergence with small group sizes while preserving general capabilities on MMLU and ARC.