Discrete Optimal Transport

Discrete optimal transport (DOT) focuses on efficiently finding the optimal way to match two discrete probability distributions, minimizing a cost function representing the "distance" between them. Current research emphasizes developing faster algorithms for solving DOT problems, particularly in dynamic settings where distributions change over time, and incorporating regularization techniques to improve efficiency and handle labeled data. These advancements are crucial for applications in machine learning, where DOT underpins tasks like generative modeling and fair resource allocation, and also for theoretical understanding of generalization bounds in machine learning models implemented on digital computers.