Error estimate for regularized optimal transport problems via Bregman divergence

TL;DR

This paper extends regularized optimal transport to Bregman divergence, providing a non-asymptotic error estimate that improves exponentially, enhancing computational efficiency and theoretical understanding.

Contribution

It introduces properties of Bregman divergence for regularized optimal transport and derives a faster-than-exponential non-asymptotic error estimate.

Findings

Error estimate becomes faster than exponential

Provides properties of Bregman divergence for optimal transport

Enhances understanding of regularized optimal transport errors

Abstract

Regularization by the Shannon entropy enables us to efficiently and approximately solve optimal transport problems on a finite set. This paper is concerned with regularized optimal transport problems via Bregman divergence. We introduce the required properties for Bregman divergences, provide a non-asymptotic error estimate for the regularized problem, and show that the error estimate becomes faster than exponentially.