A McKean-Pontrygin maximum principle for entropic-regularized optimal transport
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915903393759232 |
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| author | Reich, Sebastian |
| author_facet | Reich, Sebastian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_30019 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A McKean-Pontrygin maximum principle for entropic-regularized optimal transport Reich, Sebastian Optimization and Control Numerical Analysis 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. |
| title | A McKean-Pontrygin maximum principle for entropic-regularized optimal transport |
| topic | Optimization and Control Numerical Analysis |
| url | https://arxiv.org/abs/2603.30019 |