Robustly Learning Monotone Generalized Linear Models via Data Augmentation

Nikos Zarifis, Puqian Wang, Ilias Diakonikolas, Jelena Diakonikolas
Proceedings of Thirty Eighth Conference on Learning Theory, PMLR 291:5921-5990, 2025.

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 this Paper

BibTeX
@InProceedings{pmlr-v291-zarifis25a, 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}, pages = {5921--5990}, year = {2025}, editor = {Haghtalab, Nika and Moitra, Ankur}, volume = {291}, series = {Proceedings of Machine Learning Research}, month = {30 Jun--04 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v291/main/assets/zarifis25a/zarifis25a.pdf}, url = {https://proceedings.mlr.press/v291/zarifis25a.html}, 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.} }
Endnote
%0 Conference Paper %T Robustly Learning Monotone Generalized Linear Models via Data Augmentation %A Nikos Zarifis %A Puqian Wang %A Ilias Diakonikolas %A Jelena Diakonikolas %B Proceedings of Thirty Eighth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2025 %E Nika Haghtalab %E Ankur Moitra %F pmlr-v291-zarifis25a %I PMLR %P 5921--5990 %U https://proceedings.mlr.press/v291/zarifis25a.html %V 291 %X 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.
APA
Zarifis, N., Wang, P., Diakonikolas, I. & Diakonikolas, J.. (2025). Robustly Learning Monotone Generalized Linear Models via Data Augmentation. Proceedings of Thirty Eighth Conference on Learning Theory, in Proceedings of Machine Learning Research 291:5921-5990 Available from https://proceedings.mlr.press/v291/zarifis25a.html.

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