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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年4月7日

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  • Yumiharu Nakano,
  • Takafumi Saito

摘要

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.