# Robustly Learning Monotone Generalized Linear Models via Data Augmentation

arXiv: https://arxiv.org/abs/2502.08611 · HTML: https://mlsanity.com/paper/2502.08611/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2025.

## Built on by (most cited first, 3 of 3)

- [Robustly Learning Monotone Single-Index Models](https://mlsanity.com/paper/2508.04670/) (2025)
- [Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals](https://mlsanity.com/paper/2605.21428/) (2026)
- [Robust Regression of General ReLUs with Queries](https://mlsanity.com/paper/2606.11130/) (2026)

## Abstract (arXiv)

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 textitany 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 (Kakade et al., 2011). 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.