解决多约束指令跟随中奖励不稳定问题，提升模型遵守规则的能力。
MDP-GRPO: Stabilized Group Relative Policy Optimization for Multi-Constraint Instruction Following
- 用多温度采样增强奖励差异，避免同组奖励趋同
- 在奖励相近时仍能稳定更新，使模型更严格遵守约束
- 适合需要精确执行规则的场景，如安全对话、合规生成
基于可验证奖励的强化学习适用于多约束指令遵循任务，但标准组相对策略优化（GRPO）在离散、低方差奖励下易失稳，因组内奖励分布常高度同质。本文揭示并形式化了该情形下z-score归一化的三大问题：低方差放大、均值中心盲区和零方差崩溃。为此提出MDP-GRPO，通过（1）多温度采样提升奖励分散度，（2）双锚点优势恢复同质组梯度，消除均值中心盲区，（3）基于前景理论的奖励塑造限制更新幅度并惩罚违规，（4）非对称KL正则化。在FollowBench、IFEval及自建多约束数据集上评估，相比标准GRPO，在Llama-3.2-3B上严格满足约束能力提升最高达5.0%。方法还能在小批次下稳定收敛，同时保持在MMLU与ARC上的通用能力。
原文摘要 · Abstract (English)
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.
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