Non-rectangular Robust MDPs with Normed Uncertainty Sets

Navdeep Kumar, Adarsh Gupta, Maxence Mohamed ELFATIHI, Giorgia Ramponi, Kfir Yehuda Levy, Shie Mannor

Keywords: Robust MDPs, Non-rectangular uncertainty sets, Robust Policy evaluation

TL;DR: We propose a efficient robust policy evaluation method for non-rectangular robust MDPs with uncertainty sets bounded by $L_p$ norms.

Abstract: Robust policy evaluation for non-rectangular uncertainty set is generally NP-hard, even in approximation. Consequently, existing approaches suffer from either exponential iteration complexity or significant accuracy gaps. Interestingly, we identify a powerful class of $L_p$-bounded uncertainty sets that avoid these complexity barriers due to their structural simplicity. We further show that this class can be decomposed into infinitely many \texttt{sa}-rectangular $L_p$-bounded sets and leverage its structural properties to derive a novel dual formulation for $L_p$ robust Markov Decision Processes (MDPs). This formulation reveals key insights into the adversary’s strategy and leads to the \textbf{first polynomial-time robust policy evaluation algorithm} for $L_1$-normed non-rectangular robust MDPs.

Primary Area: Reinforcement learning (e.g., decision and control, planning, hierarchical RL, robotics)

Submission Number: 6247