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MDP-GRPO addresses critical instability issues in standard Group Relative Policy Optimization (GRPO) when handling discrete, low-dispersion rewards common in multi-constraint tasks. By introducing multi-temperature sampling, dual-anchor advantages, and prospect-theoretic shaping, the method improves strict constraint satisfaction by up to 5.0% on Llama-3.2-3B while maintaining general capabilities. This approach offers a more robust solution for reinforcement learning with verifiable rewards, particularly in scenarios requiring stable convergence with small group sizes.
MDP-GRPO: Stabilized Group Relative Policy Optimization for Multi-Constraint Instruction Following
arXiv:2606.06058v1 Announce Type: cross Abstract: 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.
Abstract: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.
Accepted to ACL 2026 Main Conference. 14 pages, 9 figures
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL)
arXiv:2606.06058 [cs.LG]
(or arXiv:2606.06058v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.06058 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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