  We consider the zeroth-order optimization problem in the huge-scale setting,
where the dimension of the problem is so large that performing even basic
vector operations on the decision variables is infeasible. In this paper, we
propose a novel algorithm, coined ZO-BCD, that exhibits favorable overall query
complexity and has a much smaller per-iteration computational complexity. In
addition, we discuss how the memory footprint of ZO-BCD can be reduced even
further by the clever use of circulant measurement matrices. As an application
of our new method, we propose the idea of crafting adversarial attacks on
neural network based classifiers in a wavelet domain, which can result in
problem dimensions of over 1.7 million. In particular, we show that crafting
adversarial examples to audio classifiers in a wavelet domain can achieve the
state-of-the-art attack success rate of 97.9%.
