Enhanced Adaptive Gradient Algorithms for Nonconvex-PL Minimax Optimization
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913801456058368 |
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| author | Huang, Feihu Xuan, Chunyu Wang, Xinrui Zhang, Siqi Chen, Songcan |
| author_facet | Huang, Feihu Xuan, Chunyu Wang, Xinrui Zhang, Siqi Chen, Songcan |
| contents | Minimax optimization recently is widely applied in many machine learning tasks such as generative adversarial networks, robust learning and reinforcement learning. In the paper, we study a class of nonconvex-nonconcave minimax optimization with nonsmooth regularization, where the objective function is possibly nonconvex on primal variable $x$, and it is nonconcave and satisfies the Polyak-Lojasiewicz (PL) condition on dual variable $y$. Moreover, we propose a class of enhanced momentum-based gradient descent ascent methods (i.e., MSGDA and AdaMSGDA) to solve these stochastic nonconvex-PL minimax problems. In particular, our AdaMSGDA algorithm can use various adaptive learning rates in updating the variables $x$ and $y$ without relying on any specifical types. Theoretically, we prove that our methods have the best known sample complexity of $\tilde{O}(ε^{-3})$ only requiring one sample at each loop in finding an $ε$-stationary solution. Some numerical experiments on PL-game and Wasserstein-GAN demonstrate the efficiency of our proposed methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_03984 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Enhanced Adaptive Gradient Algorithms for Nonconvex-PL Minimax Optimization Huang, Feihu Xuan, Chunyu Wang, Xinrui Zhang, Siqi Chen, Songcan Optimization and Control Machine Learning Numerical Analysis Minimax optimization recently is widely applied in many machine learning tasks such as generative adversarial networks, robust learning and reinforcement learning. In the paper, we study a class of nonconvex-nonconcave minimax optimization with nonsmooth regularization, where the objective function is possibly nonconvex on primal variable $x$, and it is nonconcave and satisfies the Polyak-Lojasiewicz (PL) condition on dual variable $y$. Moreover, we propose a class of enhanced momentum-based gradient descent ascent methods (i.e., MSGDA and AdaMSGDA) to solve these stochastic nonconvex-PL minimax problems. In particular, our AdaMSGDA algorithm can use various adaptive learning rates in updating the variables $x$ and $y$ without relying on any specifical types. Theoretically, we prove that our methods have the best known sample complexity of $\tilde{O}(ε^{-3})$ only requiring one sample at each loop in finding an $ε$-stationary solution. Some numerical experiments on PL-game and Wasserstein-GAN demonstrate the efficiency of our proposed methods. |
| title | Enhanced Adaptive Gradient Algorithms for Nonconvex-PL Minimax Optimization |
| topic | Optimization and Control Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2303.03984 |