A particle consensus approach to solving nonconvex-nonconcave min-max problems
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913443987062784 |
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| author | Borghi, Giacomo Huang, Hui Qiu, Jinniao |
| author_facet | Borghi, Giacomo Huang, Hui Qiu, Jinniao |
| contents | We propose a zero-order optimization method for sequential min-max problems based on two populations of interacting particles. The systems are coupled so that one population aims to solve the inner maximization problem, while the other aims to solve the outer minimization problem. The dynamics are characterized by a consensus-type interaction with additional stochasticity to promote exploration of the objective landscape. Without relying on convexity or concavity assumptions, we establish theoretical convergence guarantees of the algorithm via a suitable mean-field approximation of the particle systems. Numerical experiments illustrate the validity of the proposed approach. In particular, the algorithm is able to identify a global min-max solution, in contrast to gradient-based methods, which typically converge to possibly suboptimal stationary points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17373 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A particle consensus approach to solving nonconvex-nonconcave min-max problems Borghi, Giacomo Huang, Hui Qiu, Jinniao Optimization and Control 65C35, 65K05, 90C56, 35Q90, 35Q83 We propose a zero-order optimization method for sequential min-max problems based on two populations of interacting particles. The systems are coupled so that one population aims to solve the inner maximization problem, while the other aims to solve the outer minimization problem. The dynamics are characterized by a consensus-type interaction with additional stochasticity to promote exploration of the objective landscape. Without relying on convexity or concavity assumptions, we establish theoretical convergence guarantees of the algorithm via a suitable mean-field approximation of the particle systems. Numerical experiments illustrate the validity of the proposed approach. In particular, the algorithm is able to identify a global min-max solution, in contrast to gradient-based methods, which typically converge to possibly suboptimal stationary points. |
| title | A particle consensus approach to solving nonconvex-nonconcave min-max problems |
| topic | Optimization and Control 65C35, 65K05, 90C56, 35Q90, 35Q83 |
| url | https://arxiv.org/abs/2407.17373 |