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We tackle the problem of learning equilibria in simulation-based games. Insuch games, the players' utility functions cannot be described analytically, asthey are given through a black-box simulator that can be queried to obtainnoisy estimates of the utilities. This is the case in many real-world games inwhich a complete description of the elements involved is not available upfront,such as complex military settings and online auctions. In these situations, oneusually needs to run costly simulation processes to get an accurate estimate ofthe game outcome. As a result, solving these games begets the challenge ofdesigning learning algorithms that can find (approximate) equilibria with highconfidence, using as few simulator queries as possible. Moreover, since runningthe simulator during the game is unfeasible, the algorithms must first performa pure exploration learning phase and, then, use the (approximate) equilibriumlearned this way to play the game. In this work, we focus on two-playerzero-sum games with infinite strategy spaces. Drawing from the best armidentification literature, we design two algorithms with theoretical guaranteesto learn maximin strategies in these games. The first one works in thefixed-confidence setting, guaranteeing the desired confidence level whileminimizing the number of queries. Instead, the second algorithm fits thefixed-budget setting, maximizing the confidence without exceeding the givenmaximum number of queries. First, we formally prove {\delta}-PAC theoreticalguarantees for our algorithms under some regularity assumptions, which areencoded by letting the utility functions be drawn from a Gaussian process.Then, we experimentally evaluate our techniques on a testbed made of randomlygenerated games and instances representing simple real-world security settings.

Learning Probably Approximately Correct Maximin Strategies in Simulation-Based Games with Infinite Strategy Spaces