Multi-Objective Optimization via Wasserstein-Fisher-Rao Gradient Flow
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915028142129152 |
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| author | Ren, Yinuo Xiao, Tesi Gangwani, Tanmay Rangi, Anshuka Rahmanian, Holakou Ying, Lexing Sanyal, Subhajit |
| author_facet | Ren, Yinuo Xiao, Tesi Gangwani, Tanmay Rangi, Anshuka Rahmanian, Holakou Ying, Lexing Sanyal, Subhajit |
| contents | Multi-objective optimization (MOO) aims to optimize multiple, possibly conflicting objectives with widespread applications. We introduce a novel interacting particle method for MOO inspired by molecular dynamics simulations. Our approach combines overdamped Langevin and birth-death dynamics, incorporating a "dominance potential" to steer particles toward global Pareto optimality. In contrast to previous methods, our method is able to relocate dominated particles, making it particularly adept at managing Pareto fronts of complicated geometries. Our method is also theoretically grounded as a Wasserstein-Fisher-Rao gradient flow with convergence guarantees. Extensive experiments confirm that our approach outperforms state-of-the-art methods on challenging synthetic and real-world datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_13159 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multi-Objective Optimization via Wasserstein-Fisher-Rao Gradient Flow Ren, Yinuo Xiao, Tesi Gangwani, Tanmay Rangi, Anshuka Rahmanian, Holakou Ying, Lexing Sanyal, Subhajit Machine Learning Optimization and Control Multi-objective optimization (MOO) aims to optimize multiple, possibly conflicting objectives with widespread applications. We introduce a novel interacting particle method for MOO inspired by molecular dynamics simulations. Our approach combines overdamped Langevin and birth-death dynamics, incorporating a "dominance potential" to steer particles toward global Pareto optimality. In contrast to previous methods, our method is able to relocate dominated particles, making it particularly adept at managing Pareto fronts of complicated geometries. Our method is also theoretically grounded as a Wasserstein-Fisher-Rao gradient flow with convergence guarantees. Extensive experiments confirm that our approach outperforms state-of-the-art methods on challenging synthetic and real-world datasets. |
| title | Multi-Objective Optimization via Wasserstein-Fisher-Rao Gradient Flow |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2311.13159 |