Bregman divergence regularization of optimal transport problems on a finite set

Speaker: Asuka Takatsu

Date: Thu, Jan 26, 2023

Location: Zoom, Online

Conference: Kantorovich Initiative Seminar

Subject: Mathematics

Class: Scientific

CRG: Pacific Interdisciplinary Hub on Optimal Transport


In optimal transport problems on a finite set, one successful approach to reducing its computational burden is the regularization by the Kullback-Leibler divergence. Then a natural question arises: Are other divergences not admissible for regularization? What kinds of properties are required for divergences? I introduce required properties for Bregman divergences and provide a non-asymptotic error estimate for the optimal transport problem regularized by such Bregman divergences. This convergence is possibly faster than exponential decay as the regularized parameter goes to zero.

This talk is based on joint work with Koya Sakakibara (Okayama U. of Science) and Keiichi Morikuni (U. of Tsukuba).