A New Branch-and-Bound Pruning Framework for $\ell_0$-Regularized Problems
Abstract
We consider the resolution of learning problems involving $\ell_0$-regularization via Branch-and- Bound (BnB) algorithms. These methods explore regions of the feasible space of the problem and check whether they do not contain solutions through “pruning tests”. In standard implementations, evaluating a pruning test requires to solve a convex optimization problem, which may result in computational bottlenecks. In this paper, we present an alternative to implement pruning tests for some generic family of $\ell_0$-regularized problems. Our proposed procedure allows the simultaneous assessment of several regions and can be embedded in standard BnB implementations with a negligible computational overhead. We show through numerical simulations that our pruning strategy can improve the solving time of BnB procedures by several orders of magnitude for typical problems encountered in machine-learning applications.
Cite
Text
Guyard et al. "A New Branch-and-Bound Pruning Framework for $\ell_0$-Regularized Problems." International Conference on Machine Learning, 2024.Markdown
[Guyard et al. "A New Branch-and-Bound Pruning Framework for $\ell_0$-Regularized Problems." International Conference on Machine Learning, 2024.](https://mlanthology.org/icml/2024/guyard2024icml-new/)BibTeX
@inproceedings{guyard2024icml-new,
title = {{A New Branch-and-Bound Pruning Framework for $\ell_0$-Regularized Problems}},
author = {Guyard, Theo and Herzet, Cédric and Elvira, Clément and Arslan, Ayse-Nur},
booktitle = {International Conference on Machine Learning},
year = {2024},
pages = {48077-48096},
volume = {235},
url = {https://mlanthology.org/icml/2024/guyard2024icml-new/}
}