Minimisation of Polyak-Łojasewicz Functions Using Random Zeroth-Order Oracles
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913775709323264 |
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| author | Farzin, Amir Ali Shames, Iman |
| author_facet | Farzin, Amir Ali Shames, Iman |
| contents | The application of a zeroth-order scheme for minimising Polyak-Łojasewicz (PL) functions is considered. The framework is based on exploiting a random oracle to estimate the function gradient. The convergence of the algorithm to a global minimum in the unconstrained case and to a neighbourhood of the global minimum in the constrained case along with their corresponding complexity bounds are presented. The theoretical results are demonstrated via numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09106 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimisation of Polyak-Łojasewicz Functions Using Random Zeroth-Order Oracles Farzin, Amir Ali Shames, Iman Optimization and Control Machine Learning The application of a zeroth-order scheme for minimising Polyak-Łojasewicz (PL) functions is considered. The framework is based on exploiting a random oracle to estimate the function gradient. The convergence of the algorithm to a global minimum in the unconstrained case and to a neighbourhood of the global minimum in the constrained case along with their corresponding complexity bounds are presented. The theoretical results are demonstrated via numerical examples. |
| title | Minimisation of Polyak-Łojasewicz Functions Using Random Zeroth-Order Oracles |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2405.09106 |