Minibatch Forward-Backward-Forward Methods for Solving Stochastic Variational Inequalities

Abstract

We develop a new stochastic algorithm for solving pseudomonotone stochastic variational inequalities. Our method builds on Tseng’s forward-backward-forward algorithm, which is known in the deterministic literature to be a valuable alternative to Korpelevich’s extragradient method when solving variational inequalities over a convex and closed set governed by pseudomonotone Lipschitz continuous operators. The main computational advantage of Tseng’s algorithm is that it relies only on a single projection step and two independent queries of a stochastic oracle. Our algorithm incorporates a minibatch sampling mechanism and leads to almost sure convergence to an optimal solution. To the best of our knowledge, this is the first stochastic look-ahead algorithm achieving this by using only a single projection at each iteration.