Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods
- URL: http://arxiv.org/abs/2301.13006v2
- Date: Thu, 20 Jun 2024 15:13:25 GMT
- Title: Fast Computation of Optimal Transport via Entropy-Regularized Extragradient Methods
- Authors: Gen Li, Yanxi Chen, Yu Huang, Yuejie Chi, H. Vincent Poor, Yuxin Chen,
- Abstract summary: Efficient computation of the optimal transport distance between two distributions serves as an algorithm that empowers various applications.
This paper develops a scalable first-order optimization-based method that computes optimal transport to within $varepsilon$ additive accuracy.
- Score: 75.34939761152587
- License: http://creativecommons.org/licenses/by/4.0/
- 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 $\varepsilon$ additive accuracy with runtime $\widetilde{O}( n^2/\varepsilon)$, 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.
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