Convergence rates for regularized unbalanced optimal transport: the discrete case

TL;DR

This paper establishes convergence rates for regularized unbalanced optimal transport when comparing discrete measures, providing theoretical insights into the stability and accuracy of the method in machine learning applications.

Contribution

It offers the first theoretical convergence rates for regularized UOT in the discrete case, enhancing understanding of its stability and robustness.

Findings

Convergence rates for regularized UOT are derived.

Results demonstrate stability of solutions as regularization diminishes.

Theoretical bounds improve understanding of discrete UOT behavior.

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.