Approximate proximal-gradient methods

Anis Hamadouche, Yun Wu, Andrew M. Wallace, Joao F.C. Mota

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)
27 Downloads (Pure)

Abstract

We study the convergence of the Proximal-Gradient algorithm for convex composite problems when both the gradient and the proximal mapping are computed approximately. This scenario occurs when the gradient is computationally expensive and the proximal operator is not available in closed form and may be computed only up to a certain fixed precision. We establish tight deterministic bounds and propose new probabilistic upper bounds on the suboptimality of the function values along the iterations under some statistical assumptions on the perturbed iterates. We use the Proximal-Gradient algorithm to solve randomly generated LASSO problems while varying the fixed-point machine representation and the proximal computation precision.

Original languageEnglish
Title of host publication2021 Sensor Signal Processing for Defence Conference (SSPD): Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781665433143
ISBN (Print)9781665433150
DOIs
Publication statusPublished - 23 Sept 2021
Externally publishedYes
Event10th Sensor Signal Processing for Defence Conference, SSPD 2021 - Edinburgh, United Kingdom
Duration: 14 Sept 202115 Sept 2021

Publication series

NameSensor Signal Processing for Defence Conference (SSPD): Proceedings

Conference

Conference10th Sensor Signal Processing for Defence Conference, SSPD 2021
Country/TerritoryUnited Kingdom
CityEdinburgh
Period14/09/202115/09/2021

Bibliographical note

Funding Information:
Work supported by UK’s EPSRC (EP/T026111/1, EP/S000631/1), and the MOD University Defence Research Collaboration.

Publisher Copyright:
© 2021 IEEE.

Keywords

  • Approximate Algorithms.
  • Convex Optimization
  • Proximal Gradient

ASJC Scopus subject areas

  • Signal Processing
  • Safety, Risk, Reliability and Quality
  • Instrumentation

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