On the Convergence of Stochastic Extragradient for Bilinear Games using Restarted Iteration Averaging

TL;DR

This paper analyzes the stochastic extragradient method for bilinear games, showing that iteration averaging and restarting improve convergence to the Nash equilibrium, with theoretical guarantees and empirical validation.

Contribution

It introduces variations of the stochastic extragradient method with iteration averaging and restarting that provably enhance convergence to Nash equilibrium.

Findings

SEG with iteration averaging converges to Nash equilibrium.

Restarting improves convergence rates further.

Numerical experiments validate theoretical results.

Abstract

We study the stochastic bilinear minimax optimization problem, presenting an analysis of the same-sample Stochastic ExtraGradient (SEG) method with constant step size, and presenting variations of the method that yield favorable convergence. In sharp contrasts with the basic SEG method whose last iterate only contracts to a fixed neighborhood of the Nash equilibrium, SEG augmented with iteration averaging provably converges to the Nash equilibrium under the same standard settings, and such a rate is further improved by incorporating a scheduled restarting procedure. In the interpolation setting where noise vanishes at the Nash equilibrium, we achieve an optimal convergence rate up to tight constants. We present numerical experiments that validate our theoretical findings and demonstrate the effectiveness of the SEG method when equipped with iteration averaging and restarting.