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We study the problem of computing the minimum adversarial perturbation of theNearest Neighbor (NN) classifiers. Previous attempts either conduct attacks oncontinuous approximations of NN models or search for the perturbation by someheuristic methods. In this paper, we propose the first algorithm that is ableto compute the minimum adversarial perturbation. The main idea is to formulatethe problem as a list of convex quadratic programming (QP) problems that can beefficiently solved by the proposed algorithms for 1-NN models. Furthermore, weshow that dual solutions for these QP problems could give us a valid lowerbound of the adversarial perturbation that can be used for formal robustnessverification, giving us a nice view of attack/verification for NN models. For$K$-NN models with larger $K$, we show that the same formulation can help usefficiently compute the upper and lower bounds of the minimum adversarialperturbation, which can be used for attack and verification.

Evaluating the Robustness of Nearest Neighbor Classifiers: A Primal-Dual Perspective