  Interest in stochastic zeroth-order (SZO) methods has recently been revived
in black-box optimization scenarios such as adversarial black-box attacks to
deep neural networks. SZO methods only require the ability to evaluate the
objective function at random input points, however, their weakness is the
dependency of their convergence speed on the dimensionality of the function to
be evaluated. We present a sparse SZO optimization method that reduces this
factor to the expected dimensionality of the random perturbation during
learning. We give a proof that justifies this reduction for sparse SZO
optimization for non-convex functions without making any assumptions on
sparsity of objective function or gradient. Furthermore, we present
experimental results for neural networks on MNIST and CIFAR that show faster
convergence in training loss and test accuracy, and a smaller distance of the
gradient approximation to the true gradient in sparse SZO compared to dense
SZO.
