An Inexact Penalty Method for Fast Unbalanced Optimal Transport Optimization

Abstract

With the increasing application of optimal transport in machine learning, the unbalanced optimal transport (UOT) problem, as a variant of optimal transport, has gained attention for its improved generality. There is an urgent need for fast algorithms that can efficiently handle large penalty parameters. In this paper, we propose to use the Inexact penalty to make the Majorize-Minimization algorithm converge quickly even in UOT with large penalties. By using a dynamic scheme, we can successfully compute better and sparser solutions for the large penalty parameter and approach the computational speed of the well-known Sinkhorn algorithm, which sacrifices accuracy by adding an entropy item.