Relaxation of optimal transport problem via strictly convex functions
This work addresses a foundational problem in data sciences, offering a new relaxation approach that could enhance computational methods, though it appears incremental as it builds on existing divergence-based relaxations.
The paper tackles the optimal transport problem on finite spaces by relaxing it using strictly convex functions, particularly Bregman divergences, and provides mathematical foundations and an iterative gradient descent process for this relaxation.
An optimal transport problem on finite spaces is a linear program. Recently, a relaxation of the optimal transport problem via strictly convex functions, especially via the Kullback--Leibler divergence, sheds new light on data sciences. This paper provides the mathematical foundations and an iterative process based on a gradient descent for the relaxed optimal transport problem via Bregman divergences.