Adaptive primal-dual splitting methods for statistical learning and image processing

Thomas Goldstein, Min Li, Xiaoming Yuan

Research output: Chapter in book/report/conference proceedingConference contributionpeer-review

30 Citations (Scopus)

Abstract

The alternating direction method of multipliers (ADMM) is an important tool for solving complex optimization problems, but it involves minimization sub-steps that are often difficult to solve efficiently. The Primal-Dual Hybrid Gradient (PDHG) method is a powerful alternative that often has simpler sub-steps than ADMM, thus producing lower complexity solvers. Despite the flexibility of this method, PDHG is often impractical because it requires the careful choice of multiple stepsize parameters. There is often no intuitive way to choose these parameters to maximize efficiency, or even achieve convergence. We propose self-adaptive stepsize rules that automatically tune PDHG parameters for optimal convergence. We rigorously analyze our methods, and identify convergence rates. Numerical experiments show that adaptive PDHG has strong advantages over non-adaptive methods in terms of both efficiency and simplicity for the user.

Original languageEnglish
Title of host publication29th Annual Conference on Neural Information Processing Systems, NIPS 2015
EditorsC. Cortes, N. Lawrence, D. Lee, M. Sugiyama, R. Garnett
PublisherNeural Information Processing Systems Foundation
Pages2089-2097
Number of pages9
ISBN (Print)9781510825024
Publication statusPublished - Dec 2015
Event29th Annual Conference on Neural Information Processing Systems, NIPS 2015 - Montreal, Canada
Duration: 7 Dec 201512 Dec 2015

Publication series

NameAdvances in Neural Information Processing Systems
Volume28
ISSN (Print)1049-5258
NameNeurIPS Proceedings

Conference

Conference29th Annual Conference on Neural Information Processing Systems, NIPS 2015
Country/TerritoryCanada
CityMontreal
Period7/12/1512/12/15

Scopus Subject Areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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