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

Sebastian Reich

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arXiv · 2603.30019

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

Sebastian Reich

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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.

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Sebastian Reich. 2026-03-31. A McKean-Pontrygin maximum principle for entropic-regularized optimal transport. https://arxiv.org/abs/2603.30019

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