A Fisher-Rao gradient flow for entropic mean-field min-max games
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929502857199616 |
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| author | Lascu, Razvan-Andrei Majka, Mateusz B. Szpruch, Łukasz |
| author_facet | Lascu, Razvan-Andrei Majka, Mateusz B. Szpruch, Łukasz |
| contents | Gradient flows play a substantial role in addressing many machine learning problems. We examine the convergence in continuous-time of a \textit{Fisher-Rao} (Mean-Field Birth-Death) gradient flow in the context of solving convex-concave min-max games with entropy regularization. We propose appropriate Lyapunov functions to demonstrate convergence with explicit rates to the unique mixed Nash equilibrium. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_15834 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Fisher-Rao gradient flow for entropic mean-field min-max games Lascu, Razvan-Andrei Majka, Mateusz B. Szpruch, Łukasz Optimization and Control Machine Learning Probability Gradient flows play a substantial role in addressing many machine learning problems. We examine the convergence in continuous-time of a \textit{Fisher-Rao} (Mean-Field Birth-Death) gradient flow in the context of solving convex-concave min-max games with entropy regularization. We propose appropriate Lyapunov functions to demonstrate convergence with explicit rates to the unique mixed Nash equilibrium. |
| title | A Fisher-Rao gradient flow for entropic mean-field min-max games |
| topic | Optimization and Control Machine Learning Probability |
| url | https://arxiv.org/abs/2405.15834 |