# Solving Monge problem by Hilbert space embeddings of probability measures

arXiv: https://arxiv.org/abs/2412.03478 · HTML: https://mlsanity.com/paper/2412.03478/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2024.

## Built on by (most cited first, 1 of 1)

- [Kernel-based potential mean-field games with unbiased random Fourier U-statistics](https://mlsanity.com/paper/2605.29371/) (2026)

## Abstract (arXiv)

We propose deep learning methods for classical Monge's optimal mass transportation problems, where where the distribution constraint is treated as penalty terms 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. This is a corrected version of the ICORES 2025 proceedings paper.