Convergence of two-timescale gradient descent ascent dynamics: finite-dimensional and mean-field perspectives
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915544133795840 |
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| author | An, Jing Lu, Jianfeng |
| author_facet | An, Jing Lu, Jianfeng |
| contents | The two-timescale gradient descent-ascent (GDA) is a canonical gradient algorithm designed to find Nash equilibria in min-max games. We analyze the two-timescale GDA by investigating the effects of learning rate ratios on convergence behavior in both finite-dimensional and mean-field settings. In particular, for finite-dimensional quadratic min-max games, we obtain long-time convergence in near quasi-static regimes through the hypocoercivity method. For mean-field GDA dynamics, we investigate convergence under a finite-scale ratio using a mixed synchronous-reflection coupling technique. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_17122 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence of two-timescale gradient descent ascent dynamics: finite-dimensional and mean-field perspectives An, Jing Lu, Jianfeng Optimization and Control Machine Learning Numerical Analysis The two-timescale gradient descent-ascent (GDA) is a canonical gradient algorithm designed to find Nash equilibria in min-max games. We analyze the two-timescale GDA by investigating the effects of learning rate ratios on convergence behavior in both finite-dimensional and mean-field settings. In particular, for finite-dimensional quadratic min-max games, we obtain long-time convergence in near quasi-static regimes through the hypocoercivity method. For mean-field GDA dynamics, we investigate convergence under a finite-scale ratio using a mixed synchronous-reflection coupling technique. |
| title | Convergence of two-timescale gradient descent ascent dynamics: finite-dimensional and mean-field perspectives |
| topic | Optimization and Control Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2501.17122 |