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

Nakano, Yumiharu

doi:10.1007/s11222-026-10871-3

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

2026-04-07

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Nakano, Yumiharu *

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Saito, Takafumi

DOI：10.1007/s11222-026-10871-3

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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.

Keywords:

Multi-marginal optimal transport

Maximum mean discrepancy

Deep learning

Hilbert space embeddings of probability measures

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

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