تقرير
Momentum-based gradient descent methods for Lie groups
| العنوان: | Momentum-based gradient descent methods for Lie groups |
|---|---|
| المؤلفون: | Campos, Cédric M., de Diego, David Martín, Torrente, José |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Computer Science - Machine Learning, Mathematics - Differential Geometry, Mathematics - Numerical Analysis, 65K10 (Primary) 70G45, 22E99 (Secondary) |
| الوصف: | Polyak's Heavy Ball (PHB; Polyak, 1964), a.k.a. Classical Momentum, and Nesterov's Accelerated Gradient (NAG; Nesterov, 1983) are well know examples of momentum-descent methods for optimization. While the latter outperforms the former, solely generalizations of PHB-like methods to nonlinear spaces have been described in the literature. We propose here a generalization of NAG-like methods for Lie group optimization based on the variational one-to-one correspondence between classical and accelerated momentum methods (Campos et al., 2023). Numerical experiments are shown. Comment: 24 pages, 2 algorithms, 5 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.09363 |
| رقم الأكسشن: | edsarx.2404.09363 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |