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.

翻译：本文研究了Tsallis熵正则化最优传输问题，并讨论了当正则化参数$\varepsilon$趋近于$0$时的收敛速度。具体而言，我们利用Eckstein--Nutz发展的量化和影子论证方法，建立了Tsallis熵正则化最优传输的收敛速度。我们将此结果与基于Kullback-Leibler（KL）散度的熵正则化最优传输的收敛速度进行了比较，并表明在Tsallis相对熵意义下KL散度具有最快的收敛速度。