A Stochastic Objective-Function-Free Adaptive Regularization Method with Optimal Complexity
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910791097122816 |
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| author | Gratton, Serge Jerad, Sadok Toint, Philippe L. |
| author_facet | Gratton, Serge Jerad, Sadok Toint, Philippe L. |
| contents | A fully stochastic second-order adaptive-regularization method for unconstrained nonconvex optimization is presented which never computes the objective-function value, but yet achieves the optimal $\mathcal{O}(ε^{-3/2})$ complexity bound for finding first-order critical points. The method is noise-tolerant and the inexactness conditions required for convergence depend on the history of past steps. Applications to cases where derivative evaluation is inexact and to minimization of finite sums by sampling are discussed. Numerical experiments on large binary classification problems illustrate the potential of the new method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08018 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Stochastic Objective-Function-Free Adaptive Regularization Method with Optimal Complexity Gratton, Serge Jerad, Sadok Toint, Philippe L. Optimization and Control 49M37, 65K05, 68Q17, 68W40, 90C30 F.2.1; G.1.6; I.1.2 A fully stochastic second-order adaptive-regularization method for unconstrained nonconvex optimization is presented which never computes the objective-function value, but yet achieves the optimal $\mathcal{O}(ε^{-3/2})$ complexity bound for finding first-order critical points. The method is noise-tolerant and the inexactness conditions required for convergence depend on the history of past steps. Applications to cases where derivative evaluation is inexact and to minimization of finite sums by sampling are discussed. Numerical experiments on large binary classification problems illustrate the potential of the new method. |
| title | A Stochastic Objective-Function-Free Adaptive Regularization Method with Optimal Complexity |
| topic | Optimization and Control 49M37, 65K05, 68Q17, 68W40, 90C30 F.2.1; G.1.6; I.1.2 |
| url | https://arxiv.org/abs/2407.08018 |