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.
- Convex optimization
- Primal-dual algorithms
- Saddle point problems
- Stochastic optimization
ASJC Scopus subject areas
- Theoretical Computer Science
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- Centre for Mathematics and Algorithms for Data (MAD)
- Department of Mathematical Sciences - Proleptic Reader
Person: Research & Teaching, Researcher