Accelerating Unbalanced Optimal Transport Problem Using Dynamic Penalty Updating - Su, Xun; Kasai, Hiroyuki (Proceedings of ... International Joint Conference on Neural Networks, 2024)
With the increasing applications of Optimal Transport (OT) in the machine learning field, the Unbalanced Optimal Transport (UOT) problem, as a variant of the OT problem, 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 prove that the recently proposed Majorize-Minimization algorithm for the UOT problem can be viewed as a form of the Bregman Proximal Descent (BPD), and we propose to use the dynamic penalty updating to overcome the substantial degradation of its convergence rate in response to large penalties. Using the dynamic scheme and Nesterov acceleration of the BPD algorithm, we can successfully compute more accurate and sparser solutions for the large penalty parameter and approach the computational speed of the well-known Sinkhorn's algorithm, which sacrifices accuracy by adding an entropy item.