# A deep learning approach to multi-marginal optimal transport via Hilbert space embeddings of probability measures

arXiv: https://arxiv.org/abs/2507.09206 · HTML: https://mlsanity.com/paper/2507.09206/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jul 2025.

## Built on by (most cited first, 2 of 2)

- [Kernel-based potential mean-field games with unbiased random Fourier U-statistics](https://mlsanity.com/paper/2605.29371/) (2026)
- [Continuum-marginal optimal transport: a mesh-free kernel method](https://mlsanity.com/paper/2604.24226/) (2026)

## Abstract (arXiv)

We propose a numerical method for solving the multi-marginal Monge problem, which extends the classical Monge formulation to settings involving multiple target distributions. Our approach is based on the Hilbert space embedding of probability measures and employs a penalization technique using the maximum mean discrepancy to enforce marginal constraints. The method is designed to be computationally efficient, enabling GPU-based implementation suitable for large-scale problems. We confirm the effectiveness of the proposed method through numerical experiments using synthetic data.