On the Generalization Analysis of Adversarial Learning

Waleed Mustafa, Yunwen Lei, Marius Kloft
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:16174-16196, 2022.

Abstract

Many recent studies have highlighted the susceptibility of virtually all machine-learning models to adversarial attacks. Adversarial attacks are imperceptible changes to an input example of a given prediction model. Such changes are carefully designed to alter the otherwise correct prediction of the model. In this paper, we study the generalization properties of adversarial learning. In particular, we derive high-probability generalization bounds on the adversarial risk in terms of the empirical adversarial risk, the complexity of the function class and the adversarial noise set. Our bounds are generally applicable to many models, losses, and adversaries. We showcase its applicability by deriving adversarial generalization bounds for the multi-class classification setting and various prediction models (including linear models and Deep Neural Networks). We also derive optimistic adversarial generalization bounds for the case of smooth losses. These are the first fast-rate bounds valid for adversarial deep learning to the best of our knowledge.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-mustafa22a, title = {On the Generalization Analysis of Adversarial Learning}, author = {Mustafa, Waleed and Lei, Yunwen and Kloft, Marius}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {16174--16196}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/mustafa22a/mustafa22a.pdf}, url = {https://proceedings.mlr.press/v162/mustafa22a.html}, abstract = {Many recent studies have highlighted the susceptibility of virtually all machine-learning models to adversarial attacks. Adversarial attacks are imperceptible changes to an input example of a given prediction model. Such changes are carefully designed to alter the otherwise correct prediction of the model. In this paper, we study the generalization properties of adversarial learning. In particular, we derive high-probability generalization bounds on the adversarial risk in terms of the empirical adversarial risk, the complexity of the function class and the adversarial noise set. Our bounds are generally applicable to many models, losses, and adversaries. We showcase its applicability by deriving adversarial generalization bounds for the multi-class classification setting and various prediction models (including linear models and Deep Neural Networks). We also derive optimistic adversarial generalization bounds for the case of smooth losses. These are the first fast-rate bounds valid for adversarial deep learning to the best of our knowledge.} }
Endnote
%0 Conference Paper %T On the Generalization Analysis of Adversarial Learning %A Waleed Mustafa %A Yunwen Lei %A Marius Kloft %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-mustafa22a %I PMLR %P 16174--16196 %U https://proceedings.mlr.press/v162/mustafa22a.html %V 162 %X Many recent studies have highlighted the susceptibility of virtually all machine-learning models to adversarial attacks. Adversarial attacks are imperceptible changes to an input example of a given prediction model. Such changes are carefully designed to alter the otherwise correct prediction of the model. In this paper, we study the generalization properties of adversarial learning. In particular, we derive high-probability generalization bounds on the adversarial risk in terms of the empirical adversarial risk, the complexity of the function class and the adversarial noise set. Our bounds are generally applicable to many models, losses, and adversaries. We showcase its applicability by deriving adversarial generalization bounds for the multi-class classification setting and various prediction models (including linear models and Deep Neural Networks). We also derive optimistic adversarial generalization bounds for the case of smooth losses. These are the first fast-rate bounds valid for adversarial deep learning to the best of our knowledge.
APA
Mustafa, W., Lei, Y. & Kloft, M.. (2022). On the Generalization Analysis of Adversarial Learning. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:16174-16196 Available from https://proceedings.mlr.press/v162/mustafa22a.html.

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