تقرير
Riemannian Bilevel Optimization
| العنوان: | Riemannian Bilevel Optimization |
|---|---|
| المؤلفون: | Dutta, Sanchayan, Cheng, Xiang, Sra, Suvrit |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Computer Science - Artificial Intelligence, Computer Science - Machine Learning |
| الوصف: | We develop new algorithms for Riemannian bilevel optimization. We focus in particular on batch and stochastic gradient-based methods, with the explicit goal of avoiding second-order information such as Riemannian hyper-gradients. We propose and analyze $\mathrm{RF^2SA}$, a method that leverages first-order gradient information to navigate the complex geometry of Riemannian manifolds efficiently. Notably, $\mathrm{RF^2SA}$ is a single-loop algorithm, and thus easier to implement and use. Under various setups, including stochastic optimization, we provide explicit convergence rates for reaching $\epsilon$-stationary points. We also address the challenge of optimizing over Riemannian manifolds with constraints by adjusting the multiplier in the Lagrangian, ensuring convergence to the desired solution without requiring access to second-order derivatives. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.15816 |
| رقم الأكسشن: | edsarx.2405.15816 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |