Recent Advances in Optimal Transport for Machine Learning.

Area of Science:

• Machine Learning
• Probability Theory
• Computational Mathematics

Background:

• Optimal Transport (OT) offers a robust probabilistic framework for comparing and manipulating probability distributions.
• Its theoretical foundations have led to novel solutions in various machine learning domains.
• Applications span generative modeling, transfer learning, and more.

Purpose of the Study:

• To survey the contributions of Optimal Transport to Machine Learning from 2012 to 2023.
• To focus on OT's impact across supervised, unsupervised, transfer, and reinforcement learning.
• To highlight advancements in computational OT and its extensions.

Main Methods:

• Literature review of Optimal Transport applications in Machine Learning (2012-2023).
• Categorization of contributions based on ML sub-fields: supervised, unsupervised, transfer, and reinforcement learning.
• Analysis of recent developments in computational OT, including partial, unbalanced, Gromov, and Neural OT.

Main Results:

• Optimal Transport has significantly advanced machine learning, offering new approaches to distribution comparison and manipulation.
• The period 2012-2023 shows a surge in OT's application across diverse ML sub-fields.
• Recent computational OT developments, like Neural OT, are increasingly integrated into ML practices.

Conclusions:

• Optimal Transport is a versatile and increasingly important framework in modern Machine Learning.
• Continued research in computational OT and its extensions promises further breakthroughs.
• The interplay between OT and ML is expected to drive innovation in areas like generative models and domain adaptation.