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Theoretically Principled Trade-off between Robustness and Accuracy
Hongyang Zhang · Yaodong Yu · Jiantao Jiao · Eric Xing · Laurent El Ghaoui · Michael Jordan

Wed Jun 12 06:30 PM -- 09:00 PM (PDT) @ Pacific Ballroom #61

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.

Author Information

Hongyang Zhang (CMU & TTIC)
Yaodong Yu (University of Virginia)
Jiantao Jiao (University of California, Berkeley)
Eric Xing (Petuum Inc. and CMU)
Laurent El Ghaoui (UC Berkeley)
Michael Jordan (UC Berkeley)

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