A deep learning approach to multi-marginal optimal transport via Hilbert space embeddings of probability measures
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915385785188352 |
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| author | Nakano, Yumiharu Saito, Takafumi |
| author_facet | Nakano, Yumiharu Saito, Takafumi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09206 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A deep learning approach to multi-marginal optimal transport via Hilbert space embeddings of probability measures Nakano, Yumiharu Saito, Takafumi Optimization and Control 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. |
| title | A deep learning approach to multi-marginal optimal transport via Hilbert space embeddings of probability measures |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2507.09206 |