تقرير
Inexact subgradient methods for semialgebraic functions
| العنوان: | Inexact subgradient methods for semialgebraic functions |
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| المؤلفون: | Bolte, Jérôme, Le, Tam, Moulines, Éric, Pauwels, Edouard |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Statistics - Machine Learning |
| الوصف: | Motivated by the widespread use of approximate derivatives in machine learning and optimization, we study inexact subgradient methods with non-vanishing additive errors and step sizes. In the nonconvex semialgebraic setting, under boundedness assumptions, we prove that the method provides points that eventually fluctuate close to the critical set at a distance proportional to $\epsilon^\rho$ where $\epsilon$ is the error in subgradient evaluation and $\rho$ relates to the geometry of the problem. In the convex setting, we provide complexity results for the averaged values. We also obtain byproducts of independent interest, such as descent-like lemmas for nonsmooth nonconvex problems and some results on the limit of affine interpolants of differential inclusions. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.19517 |
| رقم الأكسشن: | edsarx.2404.19517 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |