这篇论文解决了多智能体强化学习中模型失配的难题，用分布鲁棒均值场博弈给出了严格的理论证明和算法，还给了误差界，搞博弈论和鲁棒优化的值得看。
本文针对多智能体强化学习（MARL）部署时的模型失配问题，提出无限时域平稳分布鲁棒均值场博弈框架。建立了具有压缩贝尔曼算子的鲁棒动态规划原理，通过不动点论证证明了平稳鲁棒均值场均衡的存在性。进一步给出了首个具有收敛保证的算法。将均值场解与有限人口鲁棒博弈关联，在压缩动力学下得到显式非渐近误差界。数值实验验证了多不确定性模型下的鲁棒性影响。
Stationary Robust Mean-Field Games under Model Mismatches
Deploying multi-agent reinforcement learning (MARL) in the real world is often limited by model mismatches between the training simulators and the true environment, which could be further amplified through strategic interactions and result in severe performance degradation upon deployment. Distributional robustness offers a principled response by optimizing policies against worst-case transition models drawn from an uncertainty set, but standard robust MARL frameworks become increasingly intractable as the number of agents grows. This paper develops an infinite-horizon, stationary mean-field game framework that incorporates distributional model uncertainty directly into the population-coupled dynamics. We establish a robust dynamic programming principle with a contractive Bellman operator and prove the existence of a stationary robust mean-field equilibrium via a fixed-point argument. We further develop the first concrete algorithm with convergence guarantees. We then connect the mean-field solution to a finite-population robust game whose ambiguity sets depend on the empirical distribution, showing that the mean-field equilibrium policy induces approximate equilibrium behavior as the population size increases. Under a contractive robust-dynamics regime, we further obtain explicit non-asymptotic error bounds. Numerical experiments further illustrate the qualitative and quantitative impact of robustness under multiple uncertainty models, validating our theoretical findings.