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Journal Articles Stochastic Systems Year : 2021

Minibatch forward-backward-forward methods for solving stochastic variational inequalities

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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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Dates and versions

hal-02405776 , version 1 (11-12-2019)
hal-02405776 , version 2 (07-12-2020)

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Cite

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