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arXiv · 1902.03355

Forward-backward-forward methods with variance reduction for stochastic variational inequalities

Radu Ioan Bot·Panayotis Mertikopoulos·Mathias Staudigl·Phan Tu Vuong
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Abstract

We develop a new stochastic algorithm with variance reduction for solving pseudo-monotone stochastic variational inequalities. Our method builds on Tseng's forward-backward-forward (FBF) 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 pseudo-monotone, 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 almost sure (a.s.) 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..

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Radu Ioan Bot, Panayotis Mertikopoulos, Mathias Staudigl, Phan Tu Vuong. 2019-02-09. Forward-backward-forward methods with variance reduction for stochastic variational inequalities. https://arxiv.org/abs/1902.03355

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