Explicit Regularization in Overparametrized Models via Noise Injection

Antonio Orvieto, Anant Raj, Hans Kersting, Francis Bach
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:7265-7287, 2023.

Abstract

Injecting noise within gradient descent has several desirable features, such as smoothing and regularizing properties. In this paper, we investigate the effects of injecting noise before computing a gradient step. We demonstrate that small perturbations can induce explicit regularization for simple models based on the L1-norm, group L1-norms, or nuclear norms. However, when applied to overparametrized neural networks with large widths, we show that the same perturbations can cause variance explosion. To overcome this, we propose using independent layer-wise perturbations, which provably allow for explicit regularization without variance explosion. Our empirical results show that these small perturbations lead to improved generalization performance compared to vanilla gradient descent.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-orvieto23a, title = {Explicit Regularization in Overparametrized Models via Noise Injection}, author = {Orvieto, Antonio and Raj, Anant and Kersting, Hans and Bach, Francis}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {7265--7287}, year = {2023}, editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}, volume = {206}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v206/orvieto23a/orvieto23a.pdf}, url = {https://proceedings.mlr.press/v206/orvieto23a.html}, abstract = {Injecting noise within gradient descent has several desirable features, such as smoothing and regularizing properties. In this paper, we investigate the effects of injecting noise before computing a gradient step. We demonstrate that small perturbations can induce explicit regularization for simple models based on the L1-norm, group L1-norms, or nuclear norms. However, when applied to overparametrized neural networks with large widths, we show that the same perturbations can cause variance explosion. To overcome this, we propose using independent layer-wise perturbations, which provably allow for explicit regularization without variance explosion. Our empirical results show that these small perturbations lead to improved generalization performance compared to vanilla gradient descent.} }
Endnote
%0 Conference Paper %T Explicit Regularization in Overparametrized Models via Noise Injection %A Antonio Orvieto %A Anant Raj %A Hans Kersting %A Francis Bach %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-orvieto23a %I PMLR %P 7265--7287 %U https://proceedings.mlr.press/v206/orvieto23a.html %V 206 %X Injecting noise within gradient descent has several desirable features, such as smoothing and regularizing properties. In this paper, we investigate the effects of injecting noise before computing a gradient step. We demonstrate that small perturbations can induce explicit regularization for simple models based on the L1-norm, group L1-norms, or nuclear norms. However, when applied to overparametrized neural networks with large widths, we show that the same perturbations can cause variance explosion. To overcome this, we propose using independent layer-wise perturbations, which provably allow for explicit regularization without variance explosion. Our empirical results show that these small perturbations lead to improved generalization performance compared to vanilla gradient descent.
APA
Orvieto, A., Raj, A., Kersting, H. & Bach, F.. (2023). Explicit Regularization in Overparametrized Models via Noise Injection. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:7265-7287 Available from https://proceedings.mlr.press/v206/orvieto23a.html.

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