Study of the behaviour of Nesterov Accelerated Gradient in a non convex setting: the strongly quasar convex case
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913162832379904 |
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| author | Hermant, Julien Aujol, Jean-François Dossal, Charles Rondepierre, Aude |
| author_facet | Hermant, Julien Aujol, Jean-François Dossal, Charles Rondepierre, Aude |
| contents | We study the convergence of Nesterov Accelerated Gradient (NAG) minimization algorithmapplied to a class of non convex functions called strongly quasar convex functions. We show thatNAG can achieve an accelerated convergence speed at the cost of a lower curvature assumption.We provide a continuous analysis through high resolution ODEs, where we show that despite thatnegative friction may appear, the solution of the system achieves accelerated rate of convergenceto the minimum. Finally, we identify the key geometrical property that, if dropped, theoreticallycancels the acceleration phenomenon. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19809 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Study of the behaviour of Nesterov Accelerated Gradient in a non convex setting: the strongly quasar convex case Hermant, Julien Aujol, Jean-François Dossal, Charles Rondepierre, Aude Optimization and Control We study the convergence of Nesterov Accelerated Gradient (NAG) minimization algorithmapplied to a class of non convex functions called strongly quasar convex functions. We show thatNAG can achieve an accelerated convergence speed at the cost of a lower curvature assumption.We provide a continuous analysis through high resolution ODEs, where we show that despite thatnegative friction may appear, the solution of the system achieves accelerated rate of convergenceto the minimum. Finally, we identify the key geometrical property that, if dropped, theoreticallycancels the acceleration phenomenon. |
| title | Study of the behaviour of Nesterov Accelerated Gradient in a non convex setting: the strongly quasar convex case |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2405.19809 |