Computing Optimal Transport Plans via Min-Max Gradient Flows
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915307039227904 |
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| author | Conger, Lauren Hoffmann, Franca Baptista, Ricardo Mazumdar, Eric |
| author_facet | Conger, Lauren Hoffmann, Franca Baptista, Ricardo Mazumdar, Eric |
| contents | We pose the Kantorovich optimal transport problem as a min-max problem with a Nash equilibrium that can be obtained dynamically via a two-player game, providing a framework for approximating optimal couplings. We prove convergence of the timescale-separated gradient descent dynamics to the optimal transport plan, and implement the gradient descent algorithm with a particle method, where the marginal constraints are enforced weakly using the KL divergence, automatically selecting a dynamical adaptation of the regularizer. The numerical results highlight the different advantages of using the standard Kullback-Leibler (KL) divergence versus the reverse KL divergence with this approach, opening the door for new methodologies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16890 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computing Optimal Transport Plans via Min-Max Gradient Flows Conger, Lauren Hoffmann, Franca Baptista, Ricardo Mazumdar, Eric Optimization and Control Analysis of PDEs We pose the Kantorovich optimal transport problem as a min-max problem with a Nash equilibrium that can be obtained dynamically via a two-player game, providing a framework for approximating optimal couplings. We prove convergence of the timescale-separated gradient descent dynamics to the optimal transport plan, and implement the gradient descent algorithm with a particle method, where the marginal constraints are enforced weakly using the KL divergence, automatically selecting a dynamical adaptation of the regularizer. The numerical results highlight the different advantages of using the standard Kullback-Leibler (KL) divergence versus the reverse KL divergence with this approach, opening the door for new methodologies. |
| title | Computing Optimal Transport Plans via Min-Max Gradient Flows |
| topic | Optimization and Control Analysis of PDEs |
| url | https://arxiv.org/abs/2504.16890 |