A deep learning approach to multi-marginal optimal transport via Hilbert space embeddings of probability measures
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.
Fields of Study & Subjects
Traffic Prediction and Management Techniques
Stochastic Gradient Optimization Techniques
Nuclear reactor physics and engineering
Publication details
- Journal / source
- Statistics and Computing
- Volume
- 36
- Issue
- 3
- Publication date
- 7 April 2026
- Language
- EN