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Author Chambolle, A.; Contreras, J.P.
Title Accelerated Bregman Primal-Dual Methods Applied to Optimal Transport and Wasserstein Barycenter Problems Type
Year 2023 Publication SIAM Journal on Mathematics of Data Science Abbreviated Journal SIMODS
Volume (up) 4 Issue 4 Pages 1369-1395
Keywords primal-dual method; optimal transport; Wasserstein barycenter; saddle-point
Abstract This paper discusses the efficiency of Hybrid Primal-Dual (HPD) type algorithms to approximately solve discrete Optimal Transport (OT) and Wasserstein Barycenter (WB) problems, with and without entropic regularization. Our first contribution is an analysis showing that these methods yield state-of-the-art convergence rates, both theoretically and practically. Next, we extend the HPD algorithm with the linesearch proposed by Malitsky and Pock in 2018 to the setting where the dual space has a Bregman divergence, and the dual function is relatively strongly convex to the Bregman's kernel. This extension yields a new method for OT and WB problems based on smoothing of the objective that also achieves state-of-the-art convergence rates. Finally, we introduce a new Bregman divergence based on a scaled entropy function that makes the algorithm numerically stable and reduces the smoothing, leading to sparse solutions of OT and WB problems. We complement our findings with numerical experiments and comparisons.
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ISSN 2577-0187 ISBN Medium
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Notes WOS:000978251900007 Approved
Call Number UAI @ alexi.delcanto @ Serial 1809
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