التفاصيل البيبلوغرافية
| العنوان: |
A Projection-Free Method for Solving Convex Bilevel Optimization Problems |
| المؤلفون: |
Giang-Tran, Khanh-Hung, Ho-Nguyen, Nam, Lee, Dabeen |
| سنة النشر: |
2023 |
| المجموعة: |
Mathematics |
| مصطلحات موضوعية: |
Mathematics - Optimization and Control, 90C06, 90C25, 90C30 |
| الوصف: |
When faced with multiple minima of an "inner-level" convex optimization problem, the convex bilevel optimization problem selects an optimal solution which also minimizes an auxiliary "outer-level" convex objective of interest. Bilevel optimization requires a different approach compared to single-level optimization problems since the set of minimizers for the inner-level objective is not given explicitly. In this paper, we propose a new projection-free method for convex bilevel optimization which require only a linear optimization oracle over the base domain. We establish $O(t^{-1/2})$ convergence rate guarantees for our method in terms of both inner- and outer-level objectives, and demonstrate how additional assumptions such as quadratic growth and strong convexity result in accelerated rates of up to $O(t^{-1})$ and $O(t^{-2/3})$ for inner- and outer-levels respectively. Lastly, we conduct a numerical study to demonstrate the performance of our method. |
| نوع الوثيقة: |
Working Paper |
| URL الوصول: |
http://arxiv.org/abs/2311.09738 |
| رقم الانضمام: |
edsarx.2311.09738 |
| قاعدة البيانات: |
arXiv |