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Quantitative Uniform Stability of the Iterative Proportional Fitting Procedure (2108.08129v2)
Published 18 Aug 2021 in stat.ML, cs.LG, math.OC, and math.PR
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.