Two-timescale Extragradient for Finding Local Minimax Points
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911846948143104 |
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| author | Chae, Jiseok Kim, Kyuwon Kim, Donghwan |
| author_facet | Chae, Jiseok Kim, Kyuwon Kim, Donghwan |
| contents | Minimax problems are notoriously challenging to optimize. However, we present that the two-timescale extragradient method can be a viable solution. By utilizing dynamical systems theory, we show that it converges to points that satisfy the second-order necessary condition of local minimax points, under mild conditions that the two-timescale gradient descent ascent fails to work. This work provably improves upon all previous results on finding local minimax points, by eliminating a crucial assumption that the Hessian with respect to the maximization variable is nondegenerate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_16242 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Two-timescale Extragradient for Finding Local Minimax Points Chae, Jiseok Kim, Kyuwon Kim, Donghwan Optimization and Control Machine Learning Minimax problems are notoriously challenging to optimize. However, we present that the two-timescale extragradient method can be a viable solution. By utilizing dynamical systems theory, we show that it converges to points that satisfy the second-order necessary condition of local minimax points, under mild conditions that the two-timescale gradient descent ascent fails to work. This work provably improves upon all previous results on finding local minimax points, by eliminating a crucial assumption that the Hessian with respect to the maximization variable is nondegenerate. |
| title | Two-timescale Extragradient for Finding Local Minimax Points |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2305.16242 |