Dual Regularized Optimal Transport

TL;DR

This paper introduces Dual Regularized Optimal Transport (DROT), a novel unbalanced optimal transport formulation that promotes sparsity, offers control over mass variation, and is scalable with advanced optimization methods, supported by theoretical and experimental validation.

Contribution

The paper proposes DROT, a new unbalanced optimal transport formulation with dual regularization, enabling sparse solutions and control over mass changes, and demonstrates its scalability and effectiveness.

Findings

DROT produces sparse solutions with controlled mass creation/destruction.

Theoretical analysis confirms desirable properties of DROT solutions.

Experimental results show DROT's scalability and performance at large scales.

Abstract

In this paper, we present a new formulation of unbalanced optimal transport called Dual Regularized Optimal Transport (DROT). We argue that regularizing the dual formulation of optimal transport results in a version of unbalanced optimal transport that leads to sparse solutions and that gives us control over mass creation and destruction. We build intuition behind such control and present theoretical properties of the solutions to DROT. We demonstrate that due to recent advances in optimization techniques, we can feasibly solve such a formulation at large scales and present extensive experimental evidence for this formulation and its solution.