On the convergence of stochastic forward-backward-forward algorithms with variance reduction in pseudo-monotone variational inequalities

Staudigl, Mathias ; Boţ, Radu Ioan ; Vuong, Phan Tu ; Mertikopoulos, Panayotis

URL: https://sgo-workshop.github.io/papers/11/sgo.pdf
Additional URL: https://www.researchgate.net/publication/331036968...
Document Type: Conference presentation
Year of publication: 2018
Conference title: NeurIPS 2018, Smooth Games Optimization and Machine Learning Workshop
Location of the conference venue: Montréal, Canada
Date of the conference: 07.12.2018
Related URLs:
Publication language: English
Institution: School of Business Informatics and Mathematics > Mathematical Optimization (Staudigl 2023-)
Subject: 510 Mathematics
Abstract: We develop a new stochastic algorithm with variance reduction 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 with pseudomonotone 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.
Additional information: co-located with Conference on Neural Information Processing Systems

Dieser Datensatz wurde nicht während einer Tätigkeit an der Universität Mannheim veröffentlicht, dies ist eine Externe Publikation.

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