Quantitative uniform stability of the iterative proportional fitting procedure
George Deligiannidis, Valentin De Bortoli, Arnaud Doucet
Abstract
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 Schrödinger bridges.
Topics & Concepts
Stability (learning theory)MathematicsApplied mathematicsComputer scienceMachine learningGeometric Analysis and Curvature FlowsMarkov Chains and Monte Carlo MethodsNonlinear Partial Differential Equations