Exponential convergence rate for Iterative Markovian Fitting

Abstract

We consider the discrete-time Schrödinger bridge problem on a finite state space. Although it has been known that the Iterative Markovian Fitting (IMF) algorithm converges in Kullback-Leibler divergence to the ground truth solution, the speed of that convergence remained unquantified. In this work, we establish for the first time that IMF exhibits exponential convergence with an explicit contraction factor.

Alexander Korotin

Researcher

My research interests include generative modeling, diffusion models, unpaired learning, optimal transport and Schrodinger bridges.