Year: 2025
Type: article
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 [Formula: see text] additive accuracy with runtime [Formula: see text], where [Formula: see text] 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.
Source: SIAM Journal on Optimization
DOI: 10.1137/23m1581443
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1056225131, G1469985387, G1523888516, G2376053866, Collaborative Research: CIF: Medium: Statistical and Algorithmic Foundations of Efficient Reinforcement Learning, G4720003262, RI: Small: Uncertainty Quantification for Nonconvex Low-Complexity Models, CIF: Small: Taming Nonconvexity in High-Dimensional Statistical Estimation, G5972442391, G6098521345, RI: Medium: Collaborative Research:Algorithmic High-Dimensional Statistics: Optimality, Computtional Barriers, and High-Dimensional Corrections, G8876996369
OpenAlex ID: W4411432493