Optimal Transport (OT) is a mathematical framework that first emerged in the eighteenth century and has led to a plethora of methods for answering many theoretical and applied questions. The last decade is a witness of the remarkable contributions of this classical optimization problem to machine learning. This paper is about where and how optimal transport is used in machine learning with a focus on the question of salable optimal transport. We provide a comprehensive survey of optimal transport while ensuring an accessible presentation as permitted by the nature of the topic and the context. First, we explain optimal transport background and introduce different flavors (i.e. mathematical formulations), properties, and notable applications. We then address the fundamental question of how to scale optimal transport to cope with the current demands of big and high dimensional data. We conduct a systematic analysis of the methods used in the literature for scaling OT and present the findings in a unified taxonomy. We conclude with presenting some open challenges and discussing potential future research directions. A live repository of related OT research papers is maintained in https://github.com/abdelwahed/OT_for_big_data.git.

本文讨论了在机器学习中优化传输（Optimal Transport）的应用，侧重于可扩展性问题，并提供了优化传输问题的全面综述。作者提出了现有文献中用于解决优化传输可扩展性问题的方法，并对这些方法进行了系统分析，并提出了未来研究方向和挑战。

机器学习中的最优传输综述：大数据时代的地球运动员