  We tackle the problem of learning equilibria in simulation-based games. In
such games, the players' utility functions cannot be described analytically, as
they are given through a black-box simulator that can be queried to obtain
noisy estimates of the utilities. This is the case in many real-world games in
which a complete description of the elements involved is not available upfront,
such as complex military settings and online auctions. In these situations, one
usually needs to run costly simulation processes to get an accurate estimate of
the game outcome. As a result, solving these games begets the challenge of
designing learning algorithms that can find (approximate) equilibria with high
confidence, using as few simulator queries as possible. Moreover, since running
the simulator during the game is unfeasible, the algorithms must first perform
a pure exploration learning phase and, then, use the (approximate) equilibrium
learned this way to play the game. In this work, we focus on two-player
zero-sum games with infinite strategy spaces. Drawing from the best arm
identification literature, we design two algorithms with theoretical guarantees
to learn maximin strategies in these games. The first one works in the
fixed-confidence setting, guaranteeing the desired confidence level while
minimizing the number of queries. Instead, the second algorithm fits the
fixed-budget setting, maximizing the confidence without exceeding the given
maximum number of queries. First, we formally prove {\delta}-PAC theoretical
guarantees for our algorithms under some regularity assumptions, which are
encoded by letting the utility functions be drawn from a Gaussian process.
Then, we experimentally evaluate our techniques on a testbed made of randomly
generated games and instances representing simple real-world security settings.
