  Graph neural networks (GNNs) which apply the deep neural networks to graph
data have achieved significant performance for the task of semi-supervised node
classification. However, only few work has addressed the adversarial robustness
of GNNs. In this paper, we first present a novel gradient-based attack method
that facilitates the difficulty of tackling discrete graph data. When comparing
to current adversarial attacks on GNNs, the results show that by only
perturbing a small number of edge perturbations, including addition and
deletion, our optimization-based attack can lead to a noticeable decrease in
classification performance. Moreover, leveraging our gradient-based attack, we
propose the first optimization-based adversarial training for GNNs. Our method
yields higher robustness against both different gradient based and greedy
attack methods without sacrificing classification accuracy on original graph.
