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.

翻译：本文回顾了最优传输中熵正则化的蒙日-康托罗维奇问题，并推导了计算最优传输领域若干流行算法的梯度，包括Sinkhorn算法、Wasserstein重心算法以及Wasserstein字典学习算法。