Quantitative Uniform Stability of the Iterative Proportional Fitting Procedure
Machine Learning
2021-10-25 v2 Machine Learning
Optimization and Control
Probability
Abstract
We establish the uniform in time stability, w.r.t. the marginals, of the Iterative Proportional Fitting Procedure, also known as Sinkhorn algorithm, used to solve entropy-regularised Optimal Transport problems. Our result is quantitative and stated in terms of the 1-Wasserstein metric. As a corollary we establish a quantitative stability result for Schr\"odinger bridges.
Cite
@article{arxiv.2108.08129,
title = {Quantitative Uniform Stability of the Iterative Proportional Fitting Procedure},
author = {George Deligiannidis and Valentin De Bortoli and Arnaud Doucet},
journal= {arXiv preprint arXiv:2108.08129},
year = {2021}
}
Comments
14 pages