Extragradient with player sampling for faster Nash equilibrium finding
This work addresses the computational bottleneck in large-scale multi-player game optimization, offering incremental improvements for applications like GANs.
The paper tackles the problem of finding Nash equilibria in multi-player games, such as training GANs, by proposing an extragradient method that updates a random subset of players per iteration, which provably achieves a better convergence rate than full extragradient for non-smooth convex games with noisy gradients and enables faster and better GAN training.
Data-driven modeling increasingly requires to find a Nash equilibrium in multi-player games, e.g. when training GANs. In this paper, we analyse a new extra-gradient method for Nash equilibrium finding, that performs gradient extrapolations and updates on a random subset of players at each iteration. This approach provably exhibits a better rate of convergence than full extra-gradient for non-smooth convex games with noisy gradient oracle. We propose an additional variance reduction mechanism to obtain speed-ups in smooth convex games. Our approach makes extrapolation amenable to massive multiplayer settings, and brings empirical speed-ups, in particular when using a heuristic cyclic sampling scheme. Most importantly, it allows to train faster and better GANs and mixtures of GANs.