VC Classes are Adversarially Robustly Learnable, but Only Improperly

Omar Montasser, Steve Hanneke, Nathan Srebro
Proceedings of the Thirty-Second Conference on Learning Theory, PMLR 99:2512-2530, 2019.

Abstract

We study the question of learning an adversarially robust predictor. We show that any hypothesis class $\mathcal{H}$ with finite VC dimension is robustly PAC learnable with an \emph{improper} learning rule. The requirement of being improper is necessary as we exhibit examples of hypothesis classes $\mathcal{H}$ with finite VC dimension that are \emph{not} robustly PAC learnable with any \emph{proper} learning rule.

Cite this Paper

BibTeX
@InProceedings{pmlr-v99-montasser19a, title = {VC Classes are Adversarially Robustly Learnable, but Only Improperly}, author = {Montasser, Omar and Hanneke, Steve and Srebro, Nathan}, booktitle = {Proceedings of the Thirty-Second Conference on Learning Theory}, pages = {2512--2530}, year = {2019}, editor = {Beygelzimer, Alina and Hsu, Daniel}, volume = {99}, series = {Proceedings of Machine Learning Research}, month = {25--28 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v99/montasser19a/montasser19a.pdf}, url = {https://proceedings.mlr.press/v99/montasser19a.html}, abstract = {We study the question of learning an adversarially robust predictor. We show that any hypothesis class $\mathcal{H}$ with finite VC dimension is robustly PAC learnable with an \emph{improper} learning rule. The requirement of being improper is necessary as we exhibit examples of hypothesis classes $\mathcal{H}$ with finite VC dimension that are \emph{not} robustly PAC learnable with any \emph{proper} learning rule.} }
Endnote
%0 Conference Paper %T VC Classes are Adversarially Robustly Learnable, but Only Improperly %A Omar Montasser %A Steve Hanneke %A Nathan Srebro %B Proceedings of the Thirty-Second Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2019 %E Alina Beygelzimer %E Daniel Hsu %F pmlr-v99-montasser19a %I PMLR %P 2512--2530 %U https://proceedings.mlr.press/v99/montasser19a.html %V 99 %X We study the question of learning an adversarially robust predictor. We show that any hypothesis class $\mathcal{H}$ with finite VC dimension is robustly PAC learnable with an \emph{improper} learning rule. The requirement of being improper is necessary as we exhibit examples of hypothesis classes $\mathcal{H}$ with finite VC dimension that are \emph{not} robustly PAC learnable with any \emph{proper} learning rule.
APA
Montasser, O., Hanneke, S. & Srebro, N.. (2019). VC Classes are Adversarially Robustly Learnable, but Only Improperly. Proceedings of the Thirty-Second Conference on Learning Theory, in Proceedings of Machine Learning Research 99:2512-2530 Available from https://proceedings.mlr.press/v99/montasser19a.html.

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