Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods

Abstract

Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes optimal transport to within ε additive accuracy with runtime O(n 2 /ε), where n denotes the dimension of the probability distributions of interest. Our algorithm achieves the state-of-the-art computational guarantees among all first-order methods, while exhibiting favorable numerical performance compared to classical algorithms like Sinkhorn and Greenkhorn. Underlying our algorithm designs are two key elements: (a) converting the original problem into a bilinear minimax problem over probability distributions; (b) exploiting the extragradient idea -in conjunction with entropy regularization and adaptive learning rates -to accelerate convergence.