On the Sharp Input-Output Analysis of Nonlinear Systems under Adversarial Attacks

Jihun Kim, Yuchen Fang, Javad Lavaei
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:57445-57473, 2026.

Abstract

This paper is concerned with learning the input-output mapping of general nonlinear dynamical systems. While the existing literature focuses on Gaussian inputs and benign disturbances, we significantly broaden the scope of admissible control inputs and allow correlated, nonzero-mean, adversarial disturbances. With our reformulation as a linear combination of basis functions, we prove that the $\ell_2$-norm estimator overcomes the challenges posed by an adversary with access to the full information history, provided that the attack times are sparse, i.e., the probability that the system is under adversarial attack at a given time is smaller than a certain threshold. We provide an estimation error bound that decays with the input memory length and prove its optimality by constructing a problem instance that suffers from the same bound under probabilistic adversarial attacks. Our work provides a sharp input-output analysis for a generic nonlinear and partially observed system under significantly generalized assumptions compared to existing works.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-kim26m, title = {On the Sharp Input-Output Analysis of Nonlinear Systems under Adversarial Attacks}, author = {Kim, Jihun and Fang, Yuchen and Lavaei, Javad}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {57445--57473}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/kim26m/kim26m.pdf}, url = {https://proceedings.mlr.press/v306/kim26m.html}, abstract = {This paper is concerned with learning the input-output mapping of general nonlinear dynamical systems. While the existing literature focuses on Gaussian inputs and benign disturbances, we significantly broaden the scope of admissible control inputs and allow correlated, nonzero-mean, adversarial disturbances. With our reformulation as a linear combination of basis functions, we prove that the $\ell_2$-norm estimator overcomes the challenges posed by an adversary with access to the full information history, provided that the attack times are sparse, i.e., the probability that the system is under adversarial attack at a given time is smaller than a certain threshold. We provide an estimation error bound that decays with the input memory length and prove its optimality by constructing a problem instance that suffers from the same bound under probabilistic adversarial attacks. Our work provides a sharp input-output analysis for a generic nonlinear and partially observed system under significantly generalized assumptions compared to existing works.} }
Endnote
%0 Conference Paper %T On the Sharp Input-Output Analysis of Nonlinear Systems under Adversarial Attacks %A Jihun Kim %A Yuchen Fang %A Javad Lavaei %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-kim26m %I PMLR %P 57445--57473 %U https://proceedings.mlr.press/v306/kim26m.html %V 306 %X This paper is concerned with learning the input-output mapping of general nonlinear dynamical systems. While the existing literature focuses on Gaussian inputs and benign disturbances, we significantly broaden the scope of admissible control inputs and allow correlated, nonzero-mean, adversarial disturbances. With our reformulation as a linear combination of basis functions, we prove that the $\ell_2$-norm estimator overcomes the challenges posed by an adversary with access to the full information history, provided that the attack times are sparse, i.e., the probability that the system is under adversarial attack at a given time is smaller than a certain threshold. We provide an estimation error bound that decays with the input memory length and prove its optimality by constructing a problem instance that suffers from the same bound under probabilistic adversarial attacks. Our work provides a sharp input-output analysis for a generic nonlinear and partially observed system under significantly generalized assumptions compared to existing works.
APA
Kim, J., Fang, Y. & Lavaei, J.. (2026). On the Sharp Input-Output Analysis of Nonlinear Systems under Adversarial Attacks. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:57445-57473 Available from https://proceedings.mlr.press/v306/kim26m.html.

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