Theoretically Principled Trade-off between Robustness and Accuracy

Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric Xing, Laurent El Ghaoui, Michael Jordan
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:7472-7482, 2019.

Abstract

We identify a trade-off between robustness and accuracy that serves as a guiding principle in the design of defenses against adversarial examples. Although this problem has been widely studied empirically, much remains unknown concerning the theory underlying this trade-off. In this work, we decompose the prediction error for adversarial examples (robust error) as the sum of the natural (classification) error and boundary error, and provide a differentiable upper bound using the theory of classification-calibrated loss, which is shown to be the tightest possible upper bound uniform over all probability distributions and measurable predictors. Inspired by our theoretical analysis, we also design a new defense method, TRADES, to trade adversarial robustness off against accuracy. Our proposed algorithm performs well experimentally in real-world datasets. The methodology is the foundation of our entry to the NeurIPS 2018 Adversarial Vision Challenge in which we won the 1st place out of  2,000 submissions, surpassing the runner-up approach by 11.41% in terms of mean L_2 perturbation distance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-zhang19p, title = {Theoretically Principled Trade-off between Robustness and Accuracy}, author = {Zhang, Hongyang and Yu, Yaodong and Jiao, Jiantao and Xing, Eric and Ghaoui, Laurent El and Jordan, Michael}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {7472--7482}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/zhang19p/zhang19p.pdf}, url = {https://proceedings.mlr.press/v97/zhang19p.html}, abstract = {We identify a trade-off between robustness and accuracy that serves as a guiding principle in the design of defenses against adversarial examples. Although this problem has been widely studied empirically, much remains unknown concerning the theory underlying this trade-off. In this work, we decompose the prediction error for adversarial examples (robust error) as the sum of the natural (classification) error and boundary error, and provide a differentiable upper bound using the theory of classification-calibrated loss, which is shown to be the tightest possible upper bound uniform over all probability distributions and measurable predictors. Inspired by our theoretical analysis, we also design a new defense method, TRADES, to trade adversarial robustness off against accuracy. Our proposed algorithm performs well experimentally in real-world datasets. The methodology is the foundation of our entry to the NeurIPS 2018 Adversarial Vision Challenge in which we won the 1st place out of  2,000 submissions, surpassing the runner-up approach by 11.41% in terms of mean L_2 perturbation distance.} }
Endnote
%0 Conference Paper %T Theoretically Principled Trade-off between Robustness and Accuracy %A Hongyang Zhang %A Yaodong Yu %A Jiantao Jiao %A Eric Xing %A Laurent El Ghaoui %A Michael Jordan %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-zhang19p %I PMLR %P 7472--7482 %U https://proceedings.mlr.press/v97/zhang19p.html %V 97 %X We identify a trade-off between robustness and accuracy that serves as a guiding principle in the design of defenses against adversarial examples. Although this problem has been widely studied empirically, much remains unknown concerning the theory underlying this trade-off. In this work, we decompose the prediction error for adversarial examples (robust error) as the sum of the natural (classification) error and boundary error, and provide a differentiable upper bound using the theory of classification-calibrated loss, which is shown to be the tightest possible upper bound uniform over all probability distributions and measurable predictors. Inspired by our theoretical analysis, we also design a new defense method, TRADES, to trade adversarial robustness off against accuracy. Our proposed algorithm performs well experimentally in real-world datasets. The methodology is the foundation of our entry to the NeurIPS 2018 Adversarial Vision Challenge in which we won the 1st place out of  2,000 submissions, surpassing the runner-up approach by 11.41% in terms of mean L_2 perturbation distance.
APA
Zhang, H., Yu, Y., Jiao, J., Xing, E., Ghaoui, L.E. & Jordan, M.. (2019). Theoretically Principled Trade-off between Robustness and Accuracy. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:7472-7482 Available from https://proceedings.mlr.press/v97/zhang19p.html.

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