Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new solutions to different problems in machine learning, such as generative modeling and transfer learning. In this survey we explore contributions of Optimal Transport for Machine Learning over the period 2012 -- 2023, focusing on four sub-fields of Machine Learning: supervised, unsupervised, transfer and reinforcement learning. We further highlight the recent development in computational Optimal Transport and its extensions, such as partial, unbalanced, Gromov and Neural Optimal Transport, and its interplay with Machine Learning practice.

翻译：近年来，最优传输被提出作为机器学习中比较和操作概率分布的概率框架。这源于其丰富的历史和理论，并为机器学习中的不同问题（如生成建模和迁移学习）提供了新的解决方案。本综述探讨了2012年至2023年间最优传输在机器学习中的贡献，重点关注机器学习的四个子领域：监督学习、无监督学习、迁移学习和强化学习。我们进一步强调了计算最优传输及其扩展（如部分最优传输、非平衡最优传输、Gromov最优传输和神经最优传输）的最新发展，及其与机器学习实践的相互作用。