Quantitative Uniform Stability of the Iterative Proportional Fitting Procedure
This work addresses stability issues in computational methods for Optimal Transport, which is incremental as it builds on existing algorithms to provide rigorous guarantees.
The paper tackles the problem of ensuring uniform stability over time for the Iterative Proportional Fitting Procedure (Sinkhorn algorithm) in entropy-regularized Optimal Transport, and it provides a quantitative result in terms of the 1-Wasserstein metric, with a corollary extending this to Schrödinger bridges.
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.