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

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