Optimal Extragradient-Based Algorithms for Stochastic Variational Inequalities with Separable Structure

Angela Yuan, Chris Junchi Li, Gauthier Gidel, Michael Jordan, Quanquan Gu, Simon Shaolei Du

Keywords: Stochastic variational inequalities, convex-concave separable saddle-point optimization, extragradient-based algorithm, Nesterov's acceleration, scheduled restarting, scaling reduction

Abstract: We consider the problem of solving stochastic monotone variational inequalities with a separable structure using a stochastic first-order oracle. Building on standard extragradient for variational inequalities we propose a novel algorithm---stochastic \emph{accelerated gradient-extragradient} (AG-EG)---for strongly monotone variational inequalities (VIs). Our approach combines the strengths of extragradient and Nesterov acceleration. By showing that its iterates remain in a bounded domain and applying scheduled restarting, we prove that AG-EG has an optimal convergence rate for strongly monotone VIs. Furthermore, when specializing to the particular case of bilinearly coupled strongly-convex-strongly-concave saddle-point problems, including bilinear games, our algorithm achieves fine-grained convergence rates that match the respective lower bounds, with the stochasticity being characterized by an additive statistical error term that is optimal up to a constant prefactor.

Submission Number: 1985