Non-rectangular Robust MDPs with Normed  Uncertainty Sets
Navdeep Kumar, Adarsh Gupta, Mohamed ELFATIHI, Giorgia Ramponi, Kfir Y. Levy, Shie Mannor
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 provides key insights into the adversary’s strategy and enables the development of an efficient robust policy evaluation algorithm for these $L_p$ normed non-rectangular robust MDPs.