Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications

Antonin Chambolle, Matthias Joachim Ehrhardt, Peter Richtárik, Carola-Bibiane Schönlieb

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

Abstract

We propose a stochastic extension of the primal-dual hybrid gradient algorithm studied by Chambolle and Pock in 2011 to solve saddle point problems that are separable in the dual variable. The analysis is carried out for general convex-concave saddle point problems and problems that are either partially smooth / strongly convex or fully smooth / strongly convex. We perform the analysis for arbitrary samplings of dual variables, and we obtain known deterministic results as a special case. Several variants of our stochastic method significantly outperform the deterministic variant on a variety of imaging tasks.
Original languageEnglish (US)
Pages (from-to)2783-2808
Number of pages26
JournalSIAM Journal on Optimization
Volume28
Issue number4
DOIs
StatePublished - 2017

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