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Deriving the Gradients of Some Popular Optimal Transport Algorithms

Optimization and Control 2025-12-04 v3 Data Structures and Algorithms
Authors: Fangzhou Xie
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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.

Keywords

optimal transport entropy-regularized Monge-Kantorovich Sinkhorn algorithm Wasserstein barycenter gradient computation

Cite

@article{arxiv.2504.08722,
  title  = {Deriving the Gradients of Some Popular Optimal Transport Algorithms},
  author = {Fangzhou Xie},
  journal= {arXiv preprint arXiv:2504.08722},
  year   = {2025}
}

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