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.

翻译：我们建立了时间稳定性的统一性,即边际(w.r.t.),即迭代比例适配程序(又称辛克霍恩算法)的边际,用于解决环球常规最佳运输问题。我们的结果是量化的,并以1瓦瑟斯坦标准来说明。作为必然结果,我们为Schr\'odinger桥确定了数量稳定性结果。