# Adversarial Training of Linear Models under Stealthy Attacks

arXiv: https://arxiv.org/abs/2608.25681 · HTML: https://mlsanity.com/paper/2608.25681/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 12 references that are in the map.
- First posted on arXiv 26 Aug 2026.

## Builds on (most cited first, 5 of 5)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methods](https://mlsanity.com/paper/1705.07263/) (2017)
- [Overparameterized Linear Regression under Adversarial Attacks](https://mlsanity.com/paper/2204.06274/) (2022)
- [Robust Prediction when Features are Missing](https://mlsanity.com/paper/1912.07226/) (2019)
- [Novel Stealthy Attack and Defense Strategies for Networked Control Systems](https://mlsanity.com/paper/1908.09466/) (2019)

## Abstract (arXiv)

Predictive models are widely used in many fields, but are vulnerable to false data injection attacks. To address this, detection schemes and adversarial training have been proposed, but such approaches lack guarantees against stealthy attacks. We therefore propose a detector-based switched model, in which optimal attack strategies are stealthy. For linear prediction models, we derive a convex formulation of the resulting adversarial risk. The model incorporates protected features and introduces a hyperparameter modelling attack probability, enabling an explicit performance trade-off between clean and attacked data regimes. Numerical simulations on real and synthetic data show improved performance on partially attacked data, even for misspecified attack probabilities.