Convergent Noisy forward-backward-forward algorithms in non-monotone variational inequalities

Mathias Staudigl, Panayotis Mertikopoulos

Research output: Contribution to journalConference article in journalAcademicpeer-review

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 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 with pseudo-monotone and 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 a.s. convergence to solutions of a merely pseudo-monotone stochastic variational inequality problem. To the best of our knowledge, this is the first stochastic algorithm achieving this by using only a single projection at each iteration.
Original languageEnglish
Pages (from-to)120-125
JournalIFAC-PapersOnLine
Volume52
Issue number3
DOIs
Publication statusPublished - 2019

Keywords

  • Variational inequalities
  • forward-backward-forward algorithm
  • Stochastic approximation
  • variance reduction

Cite this

@article{875f5b04ebf643029cb9736abea77258,
title = "Convergent Noisy forward-backward-forward algorithms in non-monotone variational inequalities",
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 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 with pseudo-monotone and 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 a.s. convergence to solutions of a merely pseudo-monotone stochastic variational inequality problem. To the best of our knowledge, this is the first stochastic algorithm achieving this by using only a single projection at each iteration.",
keywords = "Variational inequalities, forward-backward-forward algorithm, Stochastic approximation, variance reduction",
author = "Mathias Staudigl and Panayotis Mertikopoulos",
note = "data source:",
year = "2019",
doi = "10.1016/j.ifacol.2019.06.021",
language = "English",
volume = "52",
pages = "120--125",
journal = "IFAC-PapersOnLine",
issn = "2405-8963",
publisher = "IFAC Secretariat",
number = "3",

}

Convergent Noisy forward-backward-forward algorithms in non-monotone variational inequalities. / Staudigl, Mathias; Mertikopoulos, Panayotis.

In: IFAC-PapersOnLine, Vol. 52, No. 3, 2019, p. 120-125.

Research output: Contribution to journalConference article in journalAcademicpeer-review

TY - JOUR

T1 - Convergent Noisy forward-backward-forward algorithms in non-monotone variational inequalities

AU - Staudigl, Mathias

AU - Mertikopoulos, Panayotis

N1 - data source:

PY - 2019

Y1 - 2019

N2 - 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 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 with pseudo-monotone and 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 a.s. convergence to solutions of a merely pseudo-monotone stochastic variational inequality problem. To the best of our knowledge, this is the first stochastic algorithm achieving this by using only a single projection at each iteration.

AB - 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 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 with pseudo-monotone and 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 a.s. convergence to solutions of a merely pseudo-monotone stochastic variational inequality problem. To the best of our knowledge, this is the first stochastic algorithm achieving this by using only a single projection at each iteration.

KW - Variational inequalities

KW - forward-backward-forward algorithm

KW - Stochastic approximation

KW - variance reduction

U2 - 10.1016/j.ifacol.2019.06.021

DO - 10.1016/j.ifacol.2019.06.021

M3 - Conference article in journal

VL - 52

SP - 120

EP - 125

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8963

IS - 3

ER -