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We identify a trade-off between robustness and accuracy that serves as a guiding principle in the design of defenses against adversarial examples. Although the problem has been widely studied empirically, much remains unknown concerning the theory underlying this trade-off. In this work, we quantify the trade-off in terms of the gap between the risk for adversarial examples and the risk for non-adversarial examples. The challenge is to provide tight bounds on this quantity in terms of a surrogate loss. We give an optimal upper bound on this quantity in terms of classification-calibrated loss, which matches the lower bound in the worst case. 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 adversarial competition of a 2018 conference 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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2019 Poster: Theoretically Principled Trade-off between Robustness and Accuracy »
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