Extra-gradient with player sampling for faster convergence in n-player games
Samy Jelassi, Carles Domingo-Enrich, Damien Scieur, Arthur Mensch, Joan Bruna
Abstract
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.
BibTeX
@InProceedings{pmlr-v119-jelassi20a,
title = {Extra-gradient with player sampling for faster convergence in n-player games},
author = {Jelassi, Samy and Domingo-Enrich, Carles and Scieur, Damien and Mensch, Arthur and Bruna, Joan},
booktitle = {Proceedings of the 37th International Conference on Machine Learning},
pages = {4736--4745},
year = {2020},
editor = {III, Hal Daumé and Singh, Aarti},
volume = {119},
series = {Proceedings of Machine Learning Research},
month = {13--18 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v119/jelassi20a/jelassi20a.pdf},
url = {https://proceedings.mlr.press/v119/jelassi20a.html},
abstract = {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.}
}