4 research outputs found
Exponential Convergence of Sinkhorn Under Regularization Scheduling
In 2013, Cuturi [Cut13] introduced the Sinkhorn algorithm for matrix scaling
as a method to compute solutions to regularized optimal transport problems. In
this paper, aiming at a better convergence rate for a high accuracy solution,
we work on understanding the Sinkhorn algorithm under regularization
scheduling, and thus modify it with a mechanism that adaptively doubles the
regularization parameter periodically. We prove that such modified
version of Sinkhorn has an exponential convergence rate as iteration complexity
depending on instead of from
previous analyses [Cut13][ANWR17] in the optimal transport problems with
integral supply and demand. Furthermore, with cost and capacity scaling
procedures, the general optimal transport problem can be solved with a
logarithmic dependence on as well.Comment: ACDA23, 13 page