2025/07/01 by Denis Belomestny, Belomestny, Denis, John Schoenmakers +1
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Statistical Mechanics and Entropy #Mathematical Approximation and Integration
paper · pdf · doi:10.48550/arxiv.2507.00640
In this paper, we study the Schrödinger Bridge Problem (SBP), which is central to entropic optimal transport. For general reference processes and begin--endpoint distributions, we propose a forward-reverse iterative Monte Carlo procedure to approximate the Schrödinger potentials in a nonparametric way. In particular, we use kernel based Monte Carlo regression in the context of Picard iteration of a corresponding fixed point problem. By preserving in the iteration positivity and contractivity in a Hilbert metric sense, we develop a provably convergent algorithm. Furthermore, we provide convergence rates for the potential estimates and prove their optimality. Finally, as an application, we propose a non-nested Monte Carlo procedure for the final dimensional distributions of the Schrödinger Bridge process, based on the constructed potentials and the forward-reverse simulation method for conditional diffusions.