We develop a generic policy gradient method with the global optimality guarantee for robust Markov Decision Processes (MDPs). While policy gradient methods are widely used for solving dynamic decision problems due to their scalable and efficient nature, adapting these methods to account for model ambiguity has been challenging, often making it impractical to learn robust policies. This paper introduces a novel policy gradient method, Double-Loop Robust Policy Mirror Descent (DRPMD), for solving robust MDPs. DRPMD employs a general mirror descent update rule for the policy optimization with adaptive tolerance per iteration, guaranteeing convergence to a globally optimal policy. We provide a comprehensive analysis of DRPMD, including new convergence results under both direct and softmax parameterizations, and provide novel insights into the inner problem solution through Transition Mirror Ascent (TMA). Additionally, we propose innovative parametric transition kernels for both discrete and continuous state-action spaces, broadening the applicability of our approach. Empirical results validate the robustness and global convergence of DRPMD across various challenging robust MDP settings.

本文研究了针对稳健马尔可夫决策过程（MDPs）的策略梯度方法，填补了模型歧义对学习稳健政策的挑战。提出了一种新颖的策略梯度方法——双循环稳健政策镜面下降（DRPMD），该方法通过适应性容忍度保证了全局最优政策的收敛。实验证明了DRPMD在各种稳健MDP设定下的稳健性和全局收敛性。

稳健马尔可夫决策过程的策略梯度