Adversarially Robust Stability Certificates can be Sample-Efficient

Thomas Zhang, Stephen Tu, Nicholas Boffi, Jean-Jacques Slotine, Nikolai Matni
Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR 168:532-545, 2022.

Abstract

Motivated by bridging the simulation to reality gap in the context of safety-critical systems, we consider learning adversarially robust stability certificates for unknown nonlinear dynamical systems. In line with approaches from robust control, we consider additive and Lipschitz bounded adversaries that perturb the system dynamics. We show that under suitable assumptions of incremental stability on the underlying system, the statistical cost of learning an adversarial stability certificate is equivalent, up to constant factors, to that of learning a nominal stability certificate. Our results hinge on novel bounds for the Rademacher complexity of the resulting adversarial loss class, which may be of independent interest. To the best of our knowledge, this is the first characterization of sample-complexity bounds when performing adversarial learning over data generated by a dynamical system. We further provide a practical algorithm for approximating the adversarial training algorithm, and validate our findings on a damped pendulum example.

Cite this Paper

BibTeX
@InProceedings{pmlr-v168-zhang22a, title = {Adversarially Robust Stability Certificates can be Sample-Efficient}, author = {Zhang, Thomas and Tu, Stephen and Boffi, Nicholas and Slotine, Jean-Jacques and Matni, Nikolai}, booktitle = {Proceedings of The 4th Annual Learning for Dynamics and Control Conference}, pages = {532--545}, year = {2022}, editor = {Firoozi, Roya and Mehr, Negar and Yel, Esen and Antonova, Rika and Bohg, Jeannette and Schwager, Mac and Kochenderfer, Mykel}, volume = {168}, series = {Proceedings of Machine Learning Research}, month = {23--24 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v168/zhang22a/zhang22a.pdf}, url = {https://proceedings.mlr.press/v168/zhang22a.html}, abstract = {Motivated by bridging the simulation to reality gap in the context of safety-critical systems, we consider learning adversarially robust stability certificates for unknown nonlinear dynamical systems. In line with approaches from robust control, we consider additive and Lipschitz bounded adversaries that perturb the system dynamics. We show that under suitable assumptions of incremental stability on the underlying system, the statistical cost of learning an adversarial stability certificate is equivalent, up to constant factors, to that of learning a nominal stability certificate. Our results hinge on novel bounds for the Rademacher complexity of the resulting adversarial loss class, which may be of independent interest. To the best of our knowledge, this is the first characterization of sample-complexity bounds when performing adversarial learning over data generated by a dynamical system. We further provide a practical algorithm for approximating the adversarial training algorithm, and validate our findings on a damped pendulum example.} }
Endnote
%0 Conference Paper %T Adversarially Robust Stability Certificates can be Sample-Efficient %A Thomas Zhang %A Stephen Tu %A Nicholas Boffi %A Jean-Jacques Slotine %A Nikolai Matni %B Proceedings of The 4th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2022 %E Roya Firoozi %E Negar Mehr %E Esen Yel %E Rika Antonova %E Jeannette Bohg %E Mac Schwager %E Mykel Kochenderfer %F pmlr-v168-zhang22a %I PMLR %P 532--545 %U https://proceedings.mlr.press/v168/zhang22a.html %V 168 %X Motivated by bridging the simulation to reality gap in the context of safety-critical systems, we consider learning adversarially robust stability certificates for unknown nonlinear dynamical systems. In line with approaches from robust control, we consider additive and Lipschitz bounded adversaries that perturb the system dynamics. We show that under suitable assumptions of incremental stability on the underlying system, the statistical cost of learning an adversarial stability certificate is equivalent, up to constant factors, to that of learning a nominal stability certificate. Our results hinge on novel bounds for the Rademacher complexity of the resulting adversarial loss class, which may be of independent interest. To the best of our knowledge, this is the first characterization of sample-complexity bounds when performing adversarial learning over data generated by a dynamical system. We further provide a practical algorithm for approximating the adversarial training algorithm, and validate our findings on a damped pendulum example.
APA
Zhang, T., Tu, S., Boffi, N., Slotine, J. & Matni, N.. (2022). Adversarially Robust Stability Certificates can be Sample-Efficient. Proceedings of The 4th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 168:532-545 Available from https://proceedings.mlr.press/v168/zhang22a.html.

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