A relaxed inertial forward-backward-forward algorithm for solving monotone inclusions with application to GANs
A relaxed inertial forward-backward-forward algorithm for solving monotone inclusions with application to GANs
We introduce a relaxed inertial forward-backward-forward (RIFBF) splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitz continuous operator. This work aims to extend Tseng's forward-backward-forward method by both using inertial effects as well as relaxation parameters. We formulate first a second order dynamical system that approaches the solution set of the monotone inclusion problem to be solved and provide an asymptotic analysis for its trajectories. We provide for RIFBF, which follows by explicit time discretization, a convergence analysis in the general monotone case as well as when applied to the solving of pseudo-monotone variational inequalities. We illustrate the proposed method by applications to a bilinear saddle point problem, in the context of which we also emphasize the interplay between the inertial and the relaxation parameters, and to the training of Generative Adversarial Networks (GANs).
Bot, Radu I.
4c6d6af1-1087-4179-8d47-488f00b53d47
Sedlmayer, Michael
0bd0af16-41cd-49e4-ab2b-10563a56320e
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
1 January 2023
Bot, Radu I.
4c6d6af1-1087-4179-8d47-488f00b53d47
Sedlmayer, Michael
0bd0af16-41cd-49e4-ab2b-10563a56320e
Vuong, Phan Tu
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Bot, Radu I., Sedlmayer, Michael and Vuong, Phan Tu
(2023)
A relaxed inertial forward-backward-forward algorithm for solving monotone inclusions with application to GANs.
Journal of Machine Learning Research, 24.
Abstract
We introduce a relaxed inertial forward-backward-forward (RIFBF) splitting algorithm for approaching the set of zeros of the sum of a maximally monotone operator and a single-valued monotone and Lipschitz continuous operator. This work aims to extend Tseng's forward-backward-forward method by both using inertial effects as well as relaxation parameters. We formulate first a second order dynamical system that approaches the solution set of the monotone inclusion problem to be solved and provide an asymptotic analysis for its trajectories. We provide for RIFBF, which follows by explicit time discretization, a convergence analysis in the general monotone case as well as when applied to the solving of pseudo-monotone variational inequalities. We illustrate the proposed method by applications to a bilinear saddle point problem, in the context of which we also emphasize the interplay between the inertial and the relaxation parameters, and to the training of Generative Adversarial Networks (GANs).
More information
Accepted/In Press date: December 2022
e-pub ahead of print date: 1 January 2023
Published date: 1 January 2023
Identifiers
Local EPrints ID: 474888
URI: http://eprints.soton.ac.uk/id/eprint/474888
PURE UUID: b2085d0d-dc5d-4f30-b13a-e5097a7ae29c
Catalogue record
Date deposited: 06 Mar 2023 17:50
Last modified: 17 Mar 2024 03:58
Export record
Contributors
Author:
Radu I. Bot
Author:
Michael Sedlmayer
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
