QUANTITATIVE UNIFORM STABILITY OF THE ITERATIVE PROPORTIONAL FITTING PROCEDURE

• 成果类型: Article
• 署名作者: Deligiannidis, George; de Bortoli, Valentin; Doucet, Arnaud
• 署名单位: University of Oxford
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1970
• 发表日期: 2024
• 页码: 501-516
• 关键词: optimal transport; CONVERGENCE; geometry

摘要

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 Schrodinger bridges.