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We study the question of learning an adversarially robust predictor.
On the uniform convergence of relative frequencies of events to their probabilities
V. Vapnik and A. Chervonenkis · 1971
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On the density of families of sets
N. Sauer · 1972
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Theory of Pattern Recognition
V. Vapnik and A. Chervonenkis · 1974
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Estimation of Dependencies Based on Empirical Data
V. Vapnik · 1982
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Densité et dimension
P. Assouad · 1983
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Relating data compression and learnability
N. Littlestone and M. Warmuth · 1986
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Learnability and the Vapnik-Chervonenkis dimension
A. Blumer, A. Ehrenfeucht, D. Haussler, and M. Warmuth · 1989
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A general lower bound on the number of examples needed for learning
A. Ehrenfeucht, D. Haussler, M. Kearns, and L. Valiant · 1989
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On learning sets and functions
B. K. Natarajan · 1989
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Characterizations of learnability for classes of { 0 \{0 , . . . , n } n\} -valued functions
S. Ben-David, N. Cesa-Bianchi, D. Haussler, and P. Long · 1995
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Sample compression, learnability, and the Vapnik-Chervonenkis dimension
S. Floyd and M. Warmuth · 1995
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Weak Convergence and Empirical Processes
A. W. van der Vaart and J. A. Wellner · 1996
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Neural Network Learning: Theoretical Foundations
M. Anthony and P. L. Bartlett · 1999
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Compressing to VC dimension many points
M. Warmuth · 2003
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PAC-Bayesian compression bounds on the prediction error of learning algorithms for classification
T. Graepel, R. Herbrich, and J. Shawe-Taylor · 2005
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Stochastic convex optimization
Shai Shalev-Shwartz, Ohad Shamir, Nathan Srebro, and Karthik Sridharan · 2009
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Boosting
R. E. Schapire and Y. Freund · 2012
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Robustness and generalization
Huan Xu and Shie Mannor · 2012
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Evasion attacks against machine learning at test time
Sample compression schemes for VC classes
S. Moran and A. Yehudayoff · 2016
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Towards deep learning models resistant to adversarial attacks
Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu · 2017
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Improved generalization bounds for robust learning
Idan Attias, Aryeh Kontorovich, and Yishay Mansour · 2018
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Adversarial examples from computational constraints
Sébastien Bubeck, Eric Price, and Ilya Razenshteyn · 2018
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PAC-learning in the presence of evasion adversaries
Daniel Cullina, Arjun Nitin Bhagoji, and Prateek Mittal · 2018
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Battista Biggio, Igino Corona, Davide Maiorca, Blaine Nelson, Nedim Šrndić, Pavel Laskov, Giorgio Giacinto, and Fabio Roli · 2013
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Intriguing properties of neural networks
Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow, and Rob Fergus · 2013
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Explaining and harnessing adversarial examples
Ian J Goodfellow, Jonathon Shlens, and Christian Szegedy · 2014
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Understanding Machine Learning: From Theory to Algorithms
Shai Shalev-Shwartz and Shai Ben-David · 2014
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Multiclass learnability and the ERM principle
A. Daniely, S. Sabato, S. Ben-David, and S. Shalev-Shwartz · 2015
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Supervised learning through the lens of compression
O. David, S. Moran, and A. Yehudayoff · 2016
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Adversarial risk bounds for binary classification via function transformation
Justin Khim and Po-Ling Loh · 2018
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Foundations of machine learning
Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar · 2018
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Adversarially robust generalization requires more data
Ludwig Schmidt, Shibani Santurkar, Dimitris Tsipras, Kunal Talwar, and Aleksander Madry · 2018
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Provable defenses against adversarial examples via the convex outer adversarial polytope
Eric Wong and Zico Kolter · 2018
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Rademacher complexity for adversarially robust generalization
Dong Yin, Kannan Ramchandran, and Peter Bartlett · 2018
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Sample compression for real-valued learners
S. Hanneke, A. Kontorovich, and M. Sadigurschi · 2019
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