Policy Gradient for Robust Markov Decision Processes
This addresses the problem of robust decision-making in uncertain environments for reinforcement learning practitioners, representing a novel method for a known bottleneck rather than an incremental improvement.
The paper tackles the challenge of learning robust policies in Markov Decision Processes under model ambiguity by introducing Double-Loop Robust Policy Mirror Descent (DRPMD), a policy gradient method with global optimality guarantees, validated empirically across various settings.
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.