spred: Solving L1 Penalty with SGD

Liu Ziyin, Zihao Wang
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:43407-43422, 2023.

Abstract

We propose to minimize a generic differentiable objective with $L_1$ constraint using a simple reparametrization and straightforward stochastic gradient descent. Our proposal is the direct generalization of previous ideas that the $L_1$ penalty may be equivalent to a differentiable reparametrization with weight decay. We prove that the proposed method, spred, is an exact differentiable solver of $L_1$ and that the reparametrization trick is completely “benign" for a generic nonconvex function. Practically, we demonstrate the usefulness of the method in (1) training sparse neural networks to perform gene selection tasks, which involves finding relevant features in a very high dimensional space, and (2) neural network compression task, to which previous attempts at applying the $L_1$-penalty have been unsuccessful. Conceptually, our result bridges the gap between the sparsity in deep learning and conventional statistical learning.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-ziyin23a, title = {spred: Solving L1 Penalty with {SGD}}, author = {Ziyin, Liu and Wang, Zihao}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {43407--43422}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/ziyin23a/ziyin23a.pdf}, url = {https://proceedings.mlr.press/v202/ziyin23a.html}, abstract = {We propose to minimize a generic differentiable objective with $L_1$ constraint using a simple reparametrization and straightforward stochastic gradient descent. Our proposal is the direct generalization of previous ideas that the $L_1$ penalty may be equivalent to a differentiable reparametrization with weight decay. We prove that the proposed method, spred, is an exact differentiable solver of $L_1$ and that the reparametrization trick is completely “benign" for a generic nonconvex function. Practically, we demonstrate the usefulness of the method in (1) training sparse neural networks to perform gene selection tasks, which involves finding relevant features in a very high dimensional space, and (2) neural network compression task, to which previous attempts at applying the $L_1$-penalty have been unsuccessful. Conceptually, our result bridges the gap between the sparsity in deep learning and conventional statistical learning.} }
Endnote
%0 Conference Paper %T spred: Solving L1 Penalty with SGD %A Liu Ziyin %A Zihao Wang %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-ziyin23a %I PMLR %P 43407--43422 %U https://proceedings.mlr.press/v202/ziyin23a.html %V 202 %X We propose to minimize a generic differentiable objective with $L_1$ constraint using a simple reparametrization and straightforward stochastic gradient descent. Our proposal is the direct generalization of previous ideas that the $L_1$ penalty may be equivalent to a differentiable reparametrization with weight decay. We prove that the proposed method, spred, is an exact differentiable solver of $L_1$ and that the reparametrization trick is completely “benign" for a generic nonconvex function. Practically, we demonstrate the usefulness of the method in (1) training sparse neural networks to perform gene selection tasks, which involves finding relevant features in a very high dimensional space, and (2) neural network compression task, to which previous attempts at applying the $L_1$-penalty have been unsuccessful. Conceptually, our result bridges the gap between the sparsity in deep learning and conventional statistical learning.
APA
Ziyin, L. & Wang, Z.. (2023). spred: Solving L1 Penalty with SGD. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:43407-43422 Available from https://proceedings.mlr.press/v202/ziyin23a.html.

Related Material