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Minibatch 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 Connect in order to contact the contributor
Submitted on : Monday, December 7, 2020 - 1:39:45 PM
Last modification on : Tuesday, November 16, 2021 - 1:53:59 PM

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Radu Bot, Panayotis Mertikopoulos, Mathias Staudigl, Phan Vuong. Minibatch forward-backward-forward methods for solving stochastic variational inequalities. Stochastic Systems, INFORMS Applied Probability Society, 2021, 11 (2), pp.112-139. ⟨10.1287/stsy.2019.0064⟩. ⟨hal-02405776v2⟩

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