Convergence rates for regularized unbalanced optimal transport: the discrete case

Abstract: Unbalanced optimal transport (UOT) is a natural extension of optimal transport (OT) allowing comparison between measures of different masses. It arises naturally in machine learning by offering a robustness against outliers. The aim of this work is to provide convergence rates of the regularized transport cost and plans towards their original solution when both measures are weighted sums of Dirac masses.