{"ID":2895398,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.09206","arxiv_id":"2507.09206","title":"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.","short_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 discrepa...","url_abs":"https://arxiv.org/abs/2507.09206","url_pdf":"https://arxiv.org/pdf/2507.09206v1","authors":"[\"Yumiharu Nakano\",\"Takafumi Saito\"]","published":"2025-07-12T08:55:54Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}