A kernel-based method for Schrödinger bridges
Abstract
We characterize the Schrödinger bridge problems by a family of Mckean-Vlasov stochastic control problems with no terminal time distribution constraint. In doing so, we use the theory of Hilbert space embeddings of probability measures and then describe the constraint as penalty terms defined by the maximum mean discrepancy in the control problems. A sequence of the probability laws of the state processes resulting from $$\varepsilon $$ -optimal controls converges to a unique solution of the Schrödinger’s problem under mild conditions on given initial and terminal time distributions and an underlying diffusion process. We propose a neural SDE based deep learning algorithm for the Mckean-Vlasov stochastic control problems. Several numerical experiments validate our methods.
Fields of Study & Subjects
Image and Signal Denoising Methods
Model Reduction and Neural Networks
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- Japan Journal of Industrial and Applied Mathematics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 43
- Issue
- 2
- Publication date
- 1 June 2026
- Language
- EN