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Mini-batch forward-backward-forward methods for solving stochastic variational inequalities

Abstract : We develop a new stochastic algorithm 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 mini-batch sampling 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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https://hal.inria.fr/hal-02405776
Contributor : Panayotis Mertikopoulos <>
Submitted on : Monday, December 7, 2020 - 1:39:45 PM
Last modification on : Tuesday, December 8, 2020 - 3:30:09 AM

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  • HAL Id : hal-02405776, version 2

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Radu Bot, Panayotis Mertikopoulos, Mathias Staudigl, Phan Vuong. Mini-batch forward-backward-forward methods for solving stochastic variational inequalities. Stochastic Systems, INFORMS Applied Probability Society, In press. ⟨hal-02405776v2⟩

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