  Gradient descent and its variants are widely used in machine learning.
However, oracle access of gradient may not be available in many applications,
limiting the direct use of gradient descent. This paper proposes a method of
estimating gradient to perform gradient descent, that converges to a stationary
point for general non-convex optimization problems. Beyond the first-order
stationary properties, the second-order stationary properties are important in
machine learning applications to achieve better performance. We show that the
proposed model-free non-convex optimization algorithm returns an
$\epsilon$-second-order stationary point with
$\widetilde{O}(\frac{d^{2+\frac{\theta}{2}}}{\epsilon^{8+\theta}})$ queries of
the function for any arbitrary $\theta>0$.
