Stationary Robust Mean-Field Games under Model Mismatches

Yue Wang
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:7229-7272, 2026.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-wang26i, title = {Stationary Robust Mean-Field Games under Model Mismatches}, author = {Wang, Yue}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {7229--7272}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/wang26i/wang26i.pdf}, url = {https://proceedings.mlr.press/v337/wang26i.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Stationary Robust Mean-Field Games under Model Mismatches %A Yue Wang %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-wang26i %I PMLR %P 7229--7272 %U https://proceedings.mlr.press/v337/wang26i.html %V 337 %X 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.
APA
Wang, Y.. (2026). Stationary Robust Mean-Field Games under Model Mismatches. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:7229-7272 Available from https://proceedings.mlr.press/v337/wang26i.html.

Related Material