Robust Q-learning for Mean-Field Control under Wasserstein Uncertainty

The article introduces a robust Q-learning algorithm for discrete-time mean-field control problems with Wasserstein uncertainty in common noise. It combines quantization-and-projection with a Wasserstein dual reformulation and proves convergence with finite-time bounds for both synchronous and asynchronous schemes. Numerical experiments on systemic risk and epidemic models show the asynchronous implementation's robustness-performance tradeoff and convergence under common-noise misspecification.