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Data-driven modeling increasingly requires to find a Nash equilibrium inmulti-player games, e.g. when training GANs. In this paper, we analyse a newextra-gradient method for Nash equilibrium finding, that performs gradientextrapolations and updates on a random subset of players at each iteration.This approach provably exhibits a better rate of convergence than fullextra-gradient for non-smooth convex games with noisy gradient oracle. Wepropose an additional variance reduction mechanism to obtain speed-ups insmooth convex games. Our approach makes extrapolation amenable to massivemultiplayer settings, and brings empirical speed-ups, in particular when usinga heuristic cyclic sampling scheme. Most importantly, it allows to train fasterand better GANs and mixtures of GANs.

Extragradient with player sampling for faster Nash equilibrium finding