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  1. ; ; (, Proceedings of Machine Learning Research)
    We study robust Markov games (RMG) with 𝑠-rectangular uncertainty. We show a general equivalence between computing a robust Nash equilibrium (RNE) of a 𝑠-rectangular RMG and computing a Nash equilibrium (NE) of an appropriately constructed regularized MG. The equivalence result yields a planning algorithm for solving 𝑠-rectangular RMGs, as well as provable robustness guarantees for policies computed using regularized methods. However, we show that even for just reward-uncertain two-player zero-sum matrix games, computing an RNE is PPAD-hard. Consequently, we derive a special uncertainty structure called efficient player-decomposability and show that RNE for two-player zero-sum RMG in this class can be provably solved in polynomial time. This class includes commonly used uncertainty sets such as 𝐿1 and 𝐿∞ ball uncertainty sets. 
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