# Convergence rate of Tsallis entropic regularized optimal transport

arXiv: https://arxiv.org/abs/2304.06616 · HTML: https://mlsanity.com/paper/2304.06616/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 45 references that are in the map.
- First posted on arXiv 13 Apr 2023.

## Builds on (most cited first, 10 of 10)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [An explicit analysis of the entropic penalty in linear programming](https://mlsanity.com/paper/1806.01879/) (2018)
- [Quantitative Stability of Regularized Optimal Transport and Convergence of Sinkhorn's Algorithm](https://mlsanity.com/paper/2110.06798/) (2021)
- [Entropic Optimal Transport: Geometry and Large Deviations](https://mlsanity.com/paper/2102.04397/) (2021)
- [Tsallis Regularized Optimal Transport and Ecological Inference](https://mlsanity.com/paper/1609.04495/) (2016)
- [Convergence Rates for Regularized Optimal Transport via Quantization](https://mlsanity.com/paper/2208.14391/) (2022)
- [Optimal Transport losses and Sinkhorn algorithm with general convex regularization](https://mlsanity.com/paper/2007.00976/) (2020)
- [Convergence rate of general entropic optimal transport costs](https://mlsanity.com/paper/2206.03347/) (2022)
- [Relaxation of optimal transport problem via strictly convex functions](https://mlsanity.com/paper/2102.07336/) (2021)

## Abstract (arXiv)

In this paper, we study the Tsallis entropic regularized optimal transport in the continuous setting and establish fundamental results such as the Gamma-convergence of the Tsallis regularized optimal transport to the Monge--Kantorovich problem as the regularization parameter tends to zero. In addition, using the quantization and shadow arguments developed by Eckstein--Nutz, we derive the convergence rate of the Tsallis entropic regularization and provide explicit constants. Furthermore, we compare these results with the well-known case of the Kullback--Leibler (KL) divergence regularization and show that the KL regularization achieves the fastest convergence rate in the Tsallis framework.