这篇论文给了一个能应对不确定性干扰的Q-learning方法，在系统和疫情模型上都试过了，效果不错。
该论文提出一种鲁棒Q-learning算法，用于离散时间平均场控制问题，处理公共噪声规律中的Wasserstein不确定性。算法结合量化投影方案和Wasserstein对偶重构，并证明了同步和异步学习方案的收敛性及有限时间迭代界。在系统性风险和流行病模型上的数值实验比较了异步实现与理想Bellman迭代，展示了在公共噪声误指定下的鲁棒性-性能权衡。
Robust $Q$-learning for mean-field control under Wasserstein uncertainty in common noise
In this article, we present a robust $Q$-learning algorithm for discrete-time mean-field control problems under Wasserstein uncertainty in the common noise law. The algorithm combines a quantization-and-projection scheme with a Wasserstein dual reformulation on the common-noise space. We establish its convergence together with finite-time iteration bounds for both synchronous and asynchronous learning schemes. Numerical experiments on systemic risk and epidemic models compare the asynchronous implementation with an idealized Bellman iteration, illustrate the robustness-performance tradeoff under common-noise misspecification, and report the observed convergence behavior of the asynchronous $Q$-learning algorithm.