Quantitative Uniform Stability of the Iterative Proportional Fitting Procedure

2021/08/18 by George Deligiannidis, Valentin De Bortoli, Deligiannidis, George +3 · 1 citation
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Geometric Analysis and Curvature Flows #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods #Optimization and Control (math.OC) #Probability (math.PR) #cs.LG #math.OC #math.PR #stat.ML

paper · pdf · doi:10.48550/arxiv.2108.08129

14 pages

openalex publication_date 2021/08/18 · arxiv created 2021/10/22 · arxiv updated 2021/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Schrödinger bridges.

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• Convergence of drift-diffusion PDEs arising as Wasserstein gradient flows of convex functions

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