Stability of Schr\"odinger Potentials and Convergence of Sinkhorn's Algorithm
Probability
2022-01-26 v1 Analysis of PDEs
Functional Analysis
Optimization and Control
Abstract
We study the stability of entropically regularized optimal transport with respect to the marginals. Given marginals converging weakly, we establish a strong convergence for the Schr\"odinger potentials describing the density of the optimal couplings. When the marginals converge in total variation, the optimal couplings also converge in total variation. This is applied to show that Sinkhorn's algorithm converges in total variation when costs are quadratic and marginals are subgaussian, or more generally for all continuous costs satisfying an integrability condition.
Keywords
Cite
@article{arxiv.2201.10059,
title = {Stability of Schr\"odinger Potentials and Convergence of Sinkhorn's Algorithm},
author = {Marcel Nutz and Johannes Wiesel},
journal= {arXiv preprint arXiv:2201.10059},
year = {2022}
}