Abstract
We establish that the iterates of the iterative proportional fitting procedure, also known as Sinkhorn’s algorithm and commonly used to solve entropy-regularised optimal transport problems, are stable w.r.t. perturbations of the marginals, uniformly in time. Our result is quantitative and stated in terms of the 1-Wasserstein metric. As a corollary we establish a quantitative stability result for Schrödinger bridges.
Citation
George Deligiannidis. Valentin de Bortoli. Arnaud Doucet. "Quantitative uniform stability of the iterative proportional fitting procedure." Ann. Appl. Probab. 34 (1A) 501 - 516, February 2024. https://doi.org/10.1214/23-AAP1970
Information