A Perturbed Value-Function-Based Interior-Point Method for Perturbed Pessimistic Bilevel Problems
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914633905864704 |
|---|---|
| author | Huo, Haimei Liu, Risheng Su, Zhixun |
| author_facet | Huo, Haimei Liu, Risheng Su, Zhixun |
| contents | Bilevel optimizaiton serves as a powerful tool for many machine learning applications. Perturbed pessimistic bilevel problem PBP$ε$, with $ε$ being an arbitrary positive number, is a variant of the bilevel problem to deal with the case where there are multiple solutions in the lower level problem. However, the provably convergent algorithms for PBP$ε$ with a nonlinear lower level problem are lacking. To fill the gap, we consider in the paper the problem PBP$ε$ with a nonlinear lower level problem. By introducing a log-barrier function to replace the inequality constraint associated with the value function of the lower level problem, and approximating this value function, an algorithm named Perturbed Value-Function-based Interior-point Method(PVFIM) is proposed. We present a stationary condition for PBP$ε$, which has not been given before, and we show that PVFIM can converge to a stationary point of PBP$ε$. Finally, experiments are presented to verify the theoretical results and to show the application of the algorithm to GAN. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03636 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Perturbed Value-Function-Based Interior-Point Method for Perturbed Pessimistic Bilevel Problems Huo, Haimei Liu, Risheng Su, Zhixun Optimization and Control Bilevel optimizaiton serves as a powerful tool for many machine learning applications. Perturbed pessimistic bilevel problem PBP$ε$, with $ε$ being an arbitrary positive number, is a variant of the bilevel problem to deal with the case where there are multiple solutions in the lower level problem. However, the provably convergent algorithms for PBP$ε$ with a nonlinear lower level problem are lacking. To fill the gap, we consider in the paper the problem PBP$ε$ with a nonlinear lower level problem. By introducing a log-barrier function to replace the inequality constraint associated with the value function of the lower level problem, and approximating this value function, an algorithm named Perturbed Value-Function-based Interior-point Method(PVFIM) is proposed. We present a stationary condition for PBP$ε$, which has not been given before, and we show that PVFIM can converge to a stationary point of PBP$ε$. Finally, experiments are presented to verify the theoretical results and to show the application of the algorithm to GAN. |
| title | A Perturbed Value-Function-Based Interior-Point Method for Perturbed Pessimistic Bilevel Problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2401.03636 |