A McKean-Pontrygin maximum principle for entropic-regularized optimal transport

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.

Source: arXiv:2603.30019v1 - http://arxiv.org/abs/2603.30019v1 PDF: https://arxiv.org/pdf/2603.30019v1 Original Link: http://arxiv.org/abs/2603.30019v1