On the Convergence of Adaptive Gradient Methods for Nonconvex Optimization
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2018
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913397412462592 |
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| author | Zhou, Dongruo Chen, Jinghui Cao, Yuan Yang, Ziyan Gu, Quanquan |
| author_facet | Zhou, Dongruo Chen, Jinghui Cao, Yuan Yang, Ziyan Gu, Quanquan |
| contents | Adaptive gradient methods are workhorses in deep learning. However, the convergence guarantees of adaptive gradient methods for nonconvex optimization have not been thoroughly studied. In this paper, we provide a fine-grained convergence analysis for a general class of adaptive gradient methods including AMSGrad, RMSProp and AdaGrad. For smooth nonconvex functions, we prove that adaptive gradient methods in expectation converge to a first-order stationary point. Our convergence rate is better than existing results for adaptive gradient methods in terms of dimension. In addition, we also prove high probability bounds on the convergence rates of AMSGrad, RMSProp as well as AdaGrad, which have not been established before. Our analyses shed light on better understanding the mechanism behind adaptive gradient methods in optimizing nonconvex objectives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_05671 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On the Convergence of Adaptive Gradient Methods for Nonconvex Optimization Zhou, Dongruo Chen, Jinghui Cao, Yuan Yang, Ziyan Gu, Quanquan Machine Learning Optimization and Control Adaptive gradient methods are workhorses in deep learning. However, the convergence guarantees of adaptive gradient methods for nonconvex optimization have not been thoroughly studied. In this paper, we provide a fine-grained convergence analysis for a general class of adaptive gradient methods including AMSGrad, RMSProp and AdaGrad. For smooth nonconvex functions, we prove that adaptive gradient methods in expectation converge to a first-order stationary point. Our convergence rate is better than existing results for adaptive gradient methods in terms of dimension. In addition, we also prove high probability bounds on the convergence rates of AMSGrad, RMSProp as well as AdaGrad, which have not been established before. Our analyses shed light on better understanding the mechanism behind adaptive gradient methods in optimizing nonconvex objectives. |
| title | On the Convergence of Adaptive Gradient Methods for Nonconvex Optimization |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/1808.05671 |