On the convergence of stochastic forward- backward-forward algorithms with variance reduction in pseudo-monotone variational inequalities

Abstract

We develop a new stochastic algorithm with variance reduction 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 with pseudomonotone and 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 variance reduction mechanism, and leads to a.s. convergence to solutions of a merely pseudo-monotone stochastic variational inequality problem. To the best of our knowledge, this is the first stochastic algorithm achieving this by using only a single projection at each iteration.

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ORCID for Tu Phan: orcid.org/0000-0002-1474-994X

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