A Sinkhorn-Newton method for entropic optimal transport

TL;DR

This paper introduces a Newton-based method for solving entropic optimal transport problems, demonstrating quadratic convergence and improved performance over traditional algorithms for small regularization parameters.

Contribution

It proposes a novel Sinkhorn-Newton algorithm that enhances convergence speed and robustness in entropic optimal transport computations.

Findings

Quadratic convergence rate of the proposed method

Outperforms Sinkhorn--Knopp algorithm for small regularization

Robustness with respect to discretization parameters

Abstract

We consider the entropic regularization of discretized optimal transport and propose to solve its optimality conditions via a logarithmic Newton iteration. We show a quadratic convergence rate and validate numerically that the method compares favorably with the more commonly used Sinkhorn--Knopp algorithm for small regularization strength. We further investigate numerically the robustness of the proposed method with respect to parameters such as the mesh size of the discretization.