تقرير
Understanding Accelerated Gradient Methods: Lyapunov Analyses and Hamiltonian Assisted Interpretations
| العنوان: | Understanding Accelerated Gradient Methods: Lyapunov Analyses and Hamiltonian Assisted Interpretations |
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| المؤلفون: | Fu, Penghui, Tan, Zhiqiang |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Statistics - Machine Learning |
| الوصف: | We formulate two classes of first-order algorithms more general than previously studied for minimizing smooth and strongly convex or, respectively, smooth and convex functions. We establish sufficient conditions, via new discrete Lyapunov analyses, for achieving accelerated convergence rates which match Nesterov's methods in the strongly and general convex settings. Next, we study the convergence of limiting ordinary differential equations (ODEs) and point out currently notable gaps between the convergence properties of the corresponding algorithms and ODEs. Finally, we propose a novel class of discrete algorithms, called the Hamiltonian assisted gradient method, directly based on a Hamiltonian function and several interpretable operations, and then demonstrate meaningful and unified interpretations of our acceleration conditions. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2304.10063 |
| رقم الأكسشن: | edsarx.2304.10063 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |