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We propose a stochastic extension of the primal-dual hybrid gradientalgorithm studied by Chambolle and Pock in 2011 to solve saddle point problemsthat are separable in the dual variable. The analysis is carried out forgeneral convex-concave saddle point problems and problems that are eitherpartially smooth / strongly convex or fully smooth / strongly convex. Weperform the analysis for arbitrary samplings of dual variables, and obtainknown deterministic results as a special case. Several variants of ourstochastic method significantly outperform the deterministic variant on avariety of imaging tasks.

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