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

Minibatch forward-backward-forward methods for solving stochastic variational inequalities
Minibatch forward-backward-forward methods for solving stochastic variational inequalities
We develop a new stochastic algorithm 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 by pseudomonotone 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 minibatch sampling mechanism and leads to almost sure 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.
Boţ, Radu Ioan
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Mertikopoulos, Panayotis
741b5234-7f78-4696-8943-4aeb52f2f249
Staudigl, Mathias
78eed606-620a-4107-a1b5-2f626725db79
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Boţ, Radu Ioan
0f0d7171-17c7-47b9-bd8f-d1c00d416209
Mertikopoulos, Panayotis
741b5234-7f78-4696-8943-4aeb52f2f249
Staudigl, Mathias
78eed606-620a-4107-a1b5-2f626725db79
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf

Boţ, Radu Ioan, Mertikopoulos, Panayotis, Staudigl, Mathias and Vuong, Phan Tu (2021) Minibatch forward-backward-forward methods for solving stochastic variational inequalities. Stochastic Systems. (doi:10.1287/stsy.2019.0064).

Record type: Article

Abstract

We develop a new stochastic algorithm 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 by pseudomonotone 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 minibatch sampling mechanism and leads to almost sure 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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More information

Accepted/In Press date: 17 August 2020
e-pub ahead of print date: 25 February 2021

Identifiers

Local EPrints ID: 447524
URI: http://eprints.soton.ac.uk/id/eprint/447524
PURE UUID: 1838f04c-0459-4a17-8922-bebc552ee804
ORCID for Phan Tu Vuong: ORCID iD orcid.org/0000-0002-1474-994X

Catalogue record

Date deposited: 15 Mar 2021 17:31
Last modified: 16 Mar 2021 02:59

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Contributors

Author: Radu Ioan Boţ
Author: Panayotis Mertikopoulos
Author: Mathias Staudigl
Author: Phan Tu Vuong ORCID iD

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