Solving Monge Problem by Hilbert Space Embeddings of Probability Measures

Takafumi Saito, Yumiharu Nakano

2025

Abstract

We propose deep learning methods for classical Monge’s optimal mass transportation problems, where where the distribution constraint is treated as a penalty term defined by the maximum mean discrepancy in the theory of Hilbert space embeddings of probability measures. We prove that the transport maps given by the proposed methods converge to optimal transport maps in the problem with L2 cost. Several numerical experiments validate our methods. In particular, we show that our methods are applicable to large-scale Monge problems.

Paper Citation

in Harvard Style

Saito T. and Nakano Y. (2025). Solving Monge Problem by Hilbert Space Embeddings of Probability Measures. In Proceedings of the 14th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES; ISBN 978-989-758-732-0, SciTePress, pages 294-300. DOI: 10.5220/0013167600003893

in Bibtex Style

@conference{icores25,
author={Takafumi Saito and Yumiharu Nakano},
title={Solving Monge Problem by Hilbert Space Embeddings of Probability Measures},
booktitle={Proceedings of the 14th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES},
year={2025},
pages={294-300},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013167600003893},
isbn={978-989-758-732-0},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 14th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES
TI - Solving Monge Problem by Hilbert Space Embeddings of Probability Measures
SN - 978-989-758-732-0
AU - Saito T.
AU - Nakano Y.
PY - 2025
SP - 294
EP - 300
DO - 10.5220/0013167600003893
PB - SciTePress