Domain decomposition for entropic unbalanced optimal transport

TL;DR

This paper develops a domain decomposition method for large-scale unbalanced entropic optimal transport problems, adapting the Sinkhorn algorithm to handle the complexities of unbalanced cases efficiently.

Contribution

It introduces a novel approach to apply domain decomposition to unbalanced optimal transport, overcoming theoretical and practical challenges.

Findings

Domain decomposition is effective for large unbalanced entropic transport problems.

The adapted Sinkhorn algorithm performs efficiently on large-scale unbalanced problems.

The method is validated through experiments demonstrating scalability and efficiency.

Abstract

Solving large scale entropic optimal transport problems with the Sinkhorn algorithm remains challenging, and domain decomposition has been shown to be an efficient strategy for problems on large grids. Unbalanced optimal transport is a versatile variant of the balanced transport problem and its entropic regularization can be solved with an adapted Sinkhorn algorithm. However, it is a priori unclear how to apply domain decomposition to unbalanced problems since the independence of the cell problems is lost. In this article we show how this difficulty can be overcome at a theoretical and practical level and demonstrate with experiments that domain decomposition is also viable and efficient on large unbalanced entropic transport problems.