Value Function based Difference-of-Convex Algorithm for Bilevel Hyperparameter Selection Problems

Lucy L Gao, Jane Ye, Haian Yin, Shangzhi Zeng, Jin Zhang
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:7164-7182, 2022.

Abstract

Existing gradient-based optimization methods for hyperparameter tuning can only guarantee theoretical convergence to stationary solutions when the bilevel program satisfies the condition that for fixed upper-level variables, the lower-level is strongly convex (LLSC) and smooth (LLS). This condition is not satisfied for bilevel programs arising from tuning hyperparameters in many machine learning algorithms. In this work, we develop a sequentially convergent Value Function based Difference-of-Convex Algorithm with inexactness (VF-iDCA). We then ask: can this algorithm achieve stationary solutions without LLSC and LLS assumptions? We provide a positive answer to this question for bilevel programs from a broad class of hyperparameter tuning applications. Extensive experiments justify our theoretical results and demonstrate the superiority of the proposed VF-iDCA when applied to tune hyperparameters.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-gao22j, title = {Value Function based Difference-of-Convex Algorithm for Bilevel Hyperparameter Selection Problems}, author = {Gao, Lucy L and Ye, Jane and Yin, Haian and Zeng, Shangzhi and Zhang, Jin}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {7164--7182}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/gao22j/gao22j.pdf}, url = {https://proceedings.mlr.press/v162/gao22j.html}, abstract = {Existing gradient-based optimization methods for hyperparameter tuning can only guarantee theoretical convergence to stationary solutions when the bilevel program satisfies the condition that for fixed upper-level variables, the lower-level is strongly convex (LLSC) and smooth (LLS). This condition is not satisfied for bilevel programs arising from tuning hyperparameters in many machine learning algorithms. In this work, we develop a sequentially convergent Value Function based Difference-of-Convex Algorithm with inexactness (VF-iDCA). We then ask: can this algorithm achieve stationary solutions without LLSC and LLS assumptions? We provide a positive answer to this question for bilevel programs from a broad class of hyperparameter tuning applications. Extensive experiments justify our theoretical results and demonstrate the superiority of the proposed VF-iDCA when applied to tune hyperparameters.} }
Endnote
%0 Conference Paper %T Value Function based Difference-of-Convex Algorithm for Bilevel Hyperparameter Selection Problems %A Lucy L Gao %A Jane Ye %A Haian Yin %A Shangzhi Zeng %A Jin Zhang %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-gao22j %I PMLR %P 7164--7182 %U https://proceedings.mlr.press/v162/gao22j.html %V 162 %X Existing gradient-based optimization methods for hyperparameter tuning can only guarantee theoretical convergence to stationary solutions when the bilevel program satisfies the condition that for fixed upper-level variables, the lower-level is strongly convex (LLSC) and smooth (LLS). This condition is not satisfied for bilevel programs arising from tuning hyperparameters in many machine learning algorithms. In this work, we develop a sequentially convergent Value Function based Difference-of-Convex Algorithm with inexactness (VF-iDCA). We then ask: can this algorithm achieve stationary solutions without LLSC and LLS assumptions? We provide a positive answer to this question for bilevel programs from a broad class of hyperparameter tuning applications. Extensive experiments justify our theoretical results and demonstrate the superiority of the proposed VF-iDCA when applied to tune hyperparameters.
APA
Gao, L.L., Ye, J., Yin, H., Zeng, S. & Zhang, J.. (2022). Value Function based Difference-of-Convex Algorithm for Bilevel Hyperparameter Selection Problems. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:7164-7182 Available from https://proceedings.mlr.press/v162/gao22j.html.

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