String Diagram of Optimal Transports
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912204841811968 |
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| author | Watanabe, Kazuki Isobe, Noboru |
| author_facet | Watanabe, Kazuki Isobe, Noboru |
| contents | We present a novel hierarchical framework for optimal transport (OT) using string diagrams, namely string diagrams of optimal transports. This framework reduces complex hierarchical OT problems to standard OT problems, allowing efficient synthesis of optimal hierarchical transportation plans. Our approach uses algebraic compositions of cost matrices to effectively model hierarchical structures. We also study an adversarial situation with multiple choices in the cost matrices, where we present a polynomial-time algorithm for a relaxation of the problem. Experimental results confirm the efficiency and performance advantages of our proposed algorithm over the naive method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08550 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | String Diagram of Optimal Transports Watanabe, Kazuki Isobe, Noboru Artificial Intelligence Numerical Analysis Optimization and Control 90C05 We present a novel hierarchical framework for optimal transport (OT) using string diagrams, namely string diagrams of optimal transports. This framework reduces complex hierarchical OT problems to standard OT problems, allowing efficient synthesis of optimal hierarchical transportation plans. Our approach uses algebraic compositions of cost matrices to effectively model hierarchical structures. We also study an adversarial situation with multiple choices in the cost matrices, where we present a polynomial-time algorithm for a relaxation of the problem. Experimental results confirm the efficiency and performance advantages of our proposed algorithm over the naive method. |
| title | String Diagram of Optimal Transports |
| topic | Artificial Intelligence Numerical Analysis Optimization and Control 90C05 |
| url | https://arxiv.org/abs/2408.08550 |