Robustly Learning Monotone Generalized Linear Models via Data Augmentation
Abstract
We study the task of learning Generalized Linear models (GLMs) in the agnostic model under the Gaussian distribution. We give the first polynomial-time algorithm that achieves a constant-factor approximation for {\em any} monotone Lipschitz activation. Prior constant-factor GLM learners succeed for a substantially smaller class of activations. Our work resolves a well-known open problem, by developing a robust counterpart to the classical GLMtron algorithm \citep{kakade2011efficient}. Our robust learner applies more generally, encompassing all monotone activations with bounded $(2+\zeta)$-moments, for any fixed $\zeta>0$—a condition that is essentially necessary. To obtain our results, we leverage a novel data augmentation technique with decreasing Gaussian noise injection and prove a number of structural results that may be useful in other settings.
Cite
Text
Zarifis et al. "Robustly Learning Monotone Generalized Linear Models via Data Augmentation." Proceedings of Thirty Eighth Conference on Learning Theory, 2025.Markdown
[Zarifis et al. "Robustly Learning Monotone Generalized Linear Models via Data Augmentation." Proceedings of Thirty Eighth Conference on Learning Theory, 2025.](https://mlanthology.org/colt/2025/zarifis2025colt-robustly/)BibTeX
@inproceedings{zarifis2025colt-robustly,
title = {{Robustly Learning Monotone Generalized Linear Models via Data Augmentation}},
author = {Zarifis, Nikos and Wang, Puqian and Diakonikolas, Ilias and Diakonikolas, Jelena},
booktitle = {Proceedings of Thirty Eighth Conference on Learning Theory},
year = {2025},
pages = {5921-5990},
volume = {291},
url = {https://mlanthology.org/colt/2025/zarifis2025colt-robustly/}
}