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.

Games have a long history of serving as a benchmark for progress in artificial intelligence. Recently, approaches using search and learning have shown strong performance across a set of perfect information games, and approaches using game-theoretic reasoning and learning have shown strong performance for specific imperfect information poker variants. We introduce Player of Games, a general-purpose algorithm that unifies previous approaches, combining guided search, self-play learning, and game-theoretic reasoning. Player of Games is the first algorithm to achieve strong empirical performance in large perfect and imperfect information games -an important step towards truly general algorithms for arbitrary environments. We prove that Player of Games is sound, converging to perfect play as available computation time and approximation capacity increases. Player of Games reaches strong performance in chess and Go, beats the strongest openly available agent in heads-up no-limit Texas hold'em poker (Slumbot), and defeats the state-of-the-art agent in Scotland Yard, an imperfect information game that illustrates the value of guided search, learning, and game-theoretic reasoning.

No abstract

Researchers have shown that neural networks are vulnerable to adversarial examples and subtle environment changes. The resulting errors can look like blunders to humans, eroding trust in these agents. In prior games research, agent evaluation often focused on the in-practice game outcomes. Such evaluation typically fails to evaluate robustness to worst-case outcomes. Computer poker research has examined how to assess such worst-case performance. Unfortunately, exact computation is infeasible with larger domains, and existing approximations are poker-specific. We introduce ISMCTS-BR, a scalable search-based deep reinforcement learning algorithm for learning a best response to an agent, approximating worst-case performance. We demonstrate the technique in several games against a variety of agents, including several AlphaZero-based agents. Supplementary material is available at https://arxiv.org/abs/2004.09677.