Deriving the Gradients of Some Popular Optimal Transport Algorithms

2025/04/11 by Xie, Fangzhou
Engineering · Mathematics · Social Sciences · #Advanced Optimization Algorithms Research #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Optimization and Control (math.OC) #Traffic control and management #Transportation Planning and Optimization

paper · pdf · doi:10.48550/arxiv.2504.08722

openalex publication_date 2025/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, I review entropy-regularized Monge-Kantorovich problem in Optimal Transport, and derive the gradients of several popular algorithms popular in Computational Optimal Transport, including the Sinkhorn algorithms, Wasserstein Barycenter algorithms, and the Wasserstein Dictionary Learning algorithms.

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