A McKean-Pontrygin maximum principle for entropic-regularized optimal transport
Optimization and Control
2026-04-01 v1 Numerical Analysis
Numerical Analysis
Abstract
This note outlines a mean-field approach to dynamic optimal transport problems based on the recently proposed McKean-Pontryagin maximum principle. Key aspects of the proposed methodology include i) avoidance of sampling over stochastic paths, ii) a fully variational approach leading to constrained Hamiltonian equations of motion, and iii) a unified treatment of deterministic and stochastic optimal transport problems. We also discuss connections to well-known dynamic formulations in terms of forward-backward stochastic differential equations and extensions beyond classical entropic-regularized transport problems.
Cite
@article{arxiv.2603.30019,
title = {A McKean-Pontrygin maximum principle for entropic-regularized optimal transport},
author = {Sebastian Reich},
journal= {arXiv preprint arXiv:2603.30019},
year = {2026}
}