What type of study is this?

This is a Quantitative Study study.

October 2, 2025Open Access

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

YNYumiharu NakanoTokyo Institute of Technology TSTakafumi SaitoTokyo Institute of Technology

Key Points

The proposed method solves the multi-marginal Monge problem effectively using deep learning techniques.
It employs Hilbert space embeddings of probability measures and penalizes with maximum mean discrepancy.
This approach is computationally efficient, enabling suitable implementation for large-scale problems on GPUs.
Numerical experiments with synthetic data confirm the method's effectiveness in addressing complex target distributions.

Abstract

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.

KI fragen

Bookmark

View Full Paper