Approximate Proximal-Gradient Methods

Anis Hamadouche, Yun Wu, Andrew Michael Wallace, João F. C. Mota

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

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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)
PublisherIEEE
Pages95-100
Number of pages6
ISBN (Electronic)9781665433143
DOIs
Publication statusPublished - 15 Sep 2021
Event10th Sensor Signal Processing for Defence Conference 2021 - Edinburgh, United Kingdom
Duration: 14 Sep 202115 Sep 2021

Conference

Conference10th Sensor Signal Processing for Defence Conference 2021
Abbreviated titleSSPD 2021
Country/TerritoryUnited Kingdom
CityEdinburgh
Period14/09/2115/09/21

Keywords

  • Approximate Algorithms.
  • Convex Optimization
  • Proximal Gradient

ASJC Scopus subject areas

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

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