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In this paper, we present exploitability descent, a new algorithm to compute approximate equilibria in two-player zero-sum extensive-form games with imperfect information, by direct policy optimization against worst-case opponents. We prove that when following this optimization, the exploitability of a player's strategy converges asymptotically to zero, and hence when both players employ this optimization, the joint policies converge to a Nash equilibrium. Unlike fictitious play (XFP) and counterfactual regret minimization (CFR), our convergence result pertains to the policies being optimized rather than the average policies. Our experiments demonstrate convergence rates comparable to XFP and CFR in four benchmark games in the tabular case. Using function approximation, we find that our algorithm outperforms the tabular version in two of the games, which, to the best of our knowledge, is the first such result in imperfect information games among this class of algorithms.

We introduce DeepNash, an autonomous agent that plays the imperfect information game Stratego at a human expert level. Stratego is one of the few iconic board games that artificial intelligence (AI) has not yet mastered. It is a game characterized by a twin challenge: It requires long-term strategic thinking as in chess, but it also requires dealing with imperfect information as in poker. The technique underpinning DeepNash uses a game-theoretic, model-free deep reinforcement learning method, without search, that learns to master Stratego through self-play from scratch. DeepNash beat existing state-of-the-art AI methods in Stratego and achieved a year-to-date (2022) and all-time top-three ranking on the Gravon games platform, competing with human expert players.