Algorithms for Euclidean-regularised Optimal Transport

TL;DR

This paper investigates algorithms for Euclidean-regularized Optimal Transport, providing theoretical iteration complexity guarantees and comparing their practical efficiency through experiments on the MNIST dataset.

Contribution

It offers new theoretical analysis of several algorithms for Euclidean-regularized Optimal Transport and compares their practical performance.

Findings

Theoretical iteration complexity bounds for multiple algorithms.

Empirical performance comparison on MNIST dataset.

Insights into the efficiency of different algorithms for Euclidean-regularized OT.

Abstract

This paper addresses the Optimal Transport problem, which is regularized by the square of Euclidean $\ell_2$-norm. It offers theoretical guarantees regarding the iteration complexities of the Sinkhorn--Knopp algorithm, Accelerated Gradient Descent, Accelerated Alternating Minimisation, and Coordinate Linear Variance Reduction algorithms. Furthermore, the paper compares the practical efficiency of these methods and their counterparts when applied to the entropy-regularized Optimal Transport problem. This comparison is conducted through numerical experiments carried out on the MNIST dataset.