Applied Math Colloquium: Shiqian Ma (JHU)

Title: GPU-Accelerated Bregman Douglas-Rachford Splitting Method for Optimal Transport

Abstract: Optimal transport (OT) is a fundamental problem that finds important applications in many different fields. A popular algorithm for solving discrete optimal transport (OT) is the Sinkhorn’s algorithm. However, the Sinkhorn’s algorithm does not solve the OT problem itself. Instead, it solves its entropy-regularized approximation, and it is sensitive to the regularization parameter. In this talk, we propose the Bregman Douglas-Rachford splitting method (BDRS) for solving the OT problem, and establish its connections with existing algorithms, including the alternating direction method of multipliers (ADMM). We also show how to implement GPU-accelerated BDRS and report its performance on different OT problems. We will also discuss the convergence results of BDRS when it is treated as a matrix scaling algorithm. Some open questions regarding the global convergence of BDRS will also be discussed. 

https://shiqianma.github.io/