Convergence of ADAM for Lipschitz Objective Functions
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914713264193536 |
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| author | Ferrera, Juan Gil, Javier Gómez |
| author_facet | Ferrera, Juan Gil, Javier Gómez |
| contents | The aim of this paper is to prove the exponential convergence, local
and global, of Adam algorithm under precise conditions on the
parameters, when the objective function lacks
differentiability. More precisely, we require Lipschitz continuity,
and control on the gradient whenever it exists. We provide also
examples of interesting functions that satisfies the required
restrictions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08470 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence of ADAM for Lipschitz Objective Functions Ferrera, Juan Gil, Javier Gómez Optimization and Control Classical Analysis and ODEs Dynamical Systems 49J52 (Primary) 37N40, 46N10 (Secondary) The aim of this paper is to prove the exponential convergence, local and global, of Adam algorithm under precise conditions on the parameters, when the objective function lacks differentiability. More precisely, we require Lipschitz continuity, and control on the gradient whenever it exists. We provide also examples of interesting functions that satisfies the required restrictions. |
| title | Convergence of ADAM for Lipschitz Objective Functions |
| topic | Optimization and Control Classical Analysis and ODEs Dynamical Systems 49J52 (Primary) 37N40, 46N10 (Secondary) |
| url | https://arxiv.org/abs/2403.08470 |