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There has been substantial progress on finding game-theoretic equilibria.Most of that work has focused on games with finite, discrete action spaces.However, many games involving space, time, money, and other fine-grainedquantities have continuous action spaces (or are best modeled as such). Westudy the problem of finding an approximate Nash equilibrium of games withcontinuous action sets. The standard measure of closeness to Nash equilibriumis exploitability, which measures how much players can benefit fromunilaterally changing their strategy. We propose two new methods that minimizean approximation of the exploitability with respect to the strategy profile.The first method uses a learned best-response function, which takes the currentstrategy profile as input and returns candidate best responses for each player.The strategy profile and best-response functions are trained simultaneously,with the former trying to minimize exploitability while the latter tries tomaximize it. The second method maintains an ensemble of candidate bestresponses for each player. In each iteration, the best-performing elements ofeach ensemble are used to update the current strategy profile. The strategyprofile and best-response ensembles are simultaneously trained to minimize andmaximize the approximate exploitability, respectively. We evaluate our methodson various continuous games, showing that they outperform prior methods.

Finding Nash equilibria by minimizing approximate exploitability with learned best responses