# Mathematical Programming Approach for Adversarial Attack Modelling

### Hatem Ibn-Khedher, Mohamed Ibn Khedher, Makhlouf Hadji

#### Abstract

An adversarial attack is defined as the minimal perturbation that change the model decision. Machine learning (ML) models such as Deep Neural Networks (DNNs) are vulnerable to different adversarial examples where malicious perturbed inputs lead to erroneous model outputs. Breaking neural networks with adversarial attack requires an intelligent approach that decides about the maximum allowed margin in which the neural network decision (output) is invariant. In this paper, we propose a new formulation based on linear programming approach modelling adversarial attacks. Our approach considers noised inputs while reaching the optimal perturbation. To assess the performance of our approach, we discuss two main scenarios quantifying the algorithmâ€™s decision behavior in terms of total perturbation cost, percentage of perturbed inputs, and other cost factors. Then, the approach is implemented and evaluated under different neural network scales.

Download#### Paper Citation

#### in Harvard Style

Ibn-Khedher H., Ibn Khedher M. and Hadji M. (2021). **Mathematical Programming Approach for Adversarial Attack Modelling**.In *Proceedings of the 13th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,* ISBN 978-989-758-484-8, pages 343-350. DOI: 10.5220/0010324203430350

#### in Bibtex Style

@conference{icaart21,

author={Hatem Ibn-Khedher and Mohamed Ibn Khedher and Makhlouf Hadji},

title={Mathematical Programming Approach for Adversarial Attack Modelling},

booktitle={Proceedings of the 13th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},

year={2021},

pages={343-350},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010324203430350},

isbn={978-989-758-484-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 13th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,

TI - Mathematical Programming Approach for Adversarial Attack Modelling

SN - 978-989-758-484-8

AU - Ibn-Khedher H.

AU - Ibn Khedher M.

AU - Hadji M.

PY - 2021

SP - 343

EP - 350

DO - 10.5220/0010324203430350