  Adversarial examples are a widely studied phenomenon in machine learning
models. While most of the attention has been focused on neural networks, other
practical models also suffer from this issue. In this work, we propose an
algorithm for evaluating the adversarial robustness of $k$-nearest neighbor
classification, i.e., finding a minimum-norm adversarial example. Diverging
from previous proposals, we take a geometric approach by performing a search
that expands outwards from a given input point. On a high level, the search
radius expands to the nearby Voronoi cells until we find a cell that classifies
differently from the input point. To scale the algorithm to a large $k$, we
introduce approximation steps that find perturbations with smaller norm,
compared to the baselines, in a variety of datasets. Furthermore, we analyze
the structural properties of a dataset where our approach outperforms the
competition.
