Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications
Antonin ChambolleCMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique (Route de Saclay, 91128 Palaiseau Cedex - France)Matthias J. EhrhardtPeter RichtárikSchool of Mathematics - University of Edinburgh (University of Edinburgh Edinburgh EH9 3JZ, UK - United Kingdom)Carola‐Bibiane Schönlieb
2018en
ABI
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.
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