  In this paper, we consider Tsallis entropic regularized optimal transport and
discuss the convergence rate as the regularization parameter $\varepsilon$ 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.
