Convergence rate of Tsallis entropic regularized optimal transport

04/13/2023

∙

by   Takeshi Suguro, et al.

∙

0

∙

share

In this paper, we consider Tsallis entropic regularized optimal transport and discuss the convergence rate as the regularization parameter ε goes to 0. In particular, we establish the convergence rate of the Tsallis entropic regularized optimal transport using the quantization and shadow arguments developed by Eckstein–Nutz. We compare this to the convergence rate of the entropic regularized optimal transport with Kullback–Leibler (KL) divergence and show that KL is the fastest convergence rate in terms of Tsallis relative entropy.