Lower-level Duality Based Reformulation and Majorization Minimization Algorithm for Hyperparameter Optimization
He Chen, Haochen Xu, Rujun Jiang, Anthony Man-Cho So
Abstract
Hyperparameter tuning is an important task of machine learning, which can be formulated as a bilevel program (BLP). However, most existing algorithms are not applicable for BLP with non-smooth lower-level problems. To address this, we propose a single-level reformulation of the BLP based on lower-level duality without involving any implicit value function. To solve the reformulation, we propose a majorization minimization algorithm that marjorizes the constraint in each iteration. Furthermore, we show that the subproblems of the proposed algorithm for several widely-used hyperparameter turning models can be reformulated into conic programs that can be efficiently solved by the off-the-shelf solvers. We theoretically prove the convergence of the proposed algorithm and demonstrate its superiority through numerical experiments.
BibTeX
@InProceedings{pmlr-v238-chen24a,
title = {Lower-level Duality Based Reformulation and Majorization Minimization Algorithm for Hyperparameter Optimization},
author = {Chen, He and Xu, Haochen and Jiang, Rujun and Man-Cho So, Anthony},
booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics},
pages = {784--792},
year = {2024},
editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen},
volume = {238},
series = {Proceedings of Machine Learning Research},
month = {02--04 May},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v238/chen24a/chen24a.pdf},
url = {https://proceedings.mlr.press/v238/chen24a.html},
abstract = {Hyperparameter tuning is an important task of machine learning, which can be formulated as a bilevel program (BLP). However, most existing algorithms are not applicable for BLP with non-smooth lower-level problems. To address this, we propose a single-level reformulation of the BLP based on lower-level duality without involving any implicit value function. To solve the reformulation, we propose a majorization minimization algorithm that marjorizes the constraint in each iteration. Furthermore, we show that the subproblems of the proposed algorithm for several widely-used hyperparameter turning models can be reformulated into conic programs that can be efficiently solved by the off-the-shelf solvers. We theoretically prove the convergence of the proposed algorithm and demonstrate its superiority through numerical experiments.}
}