  In this paper we study stochastic quasi-Newton methods for nonconvex
stochastic optimization, where we assume that noisy information about the
gradients of the objective function is available via a stochastic first-order
oracle (SFO). We propose a general framework for such methods, for which we
prove almost sure convergence to stationary points and analyze its worst-case
iteration complexity. When a randomly chosen iterate is returned as the output
of such an algorithm, we prove that in the worst-case, the SFO-calls complexity
is $O(\epsilon^{-2})$ to ensure that the expectation of the squared norm of the
gradient is smaller than the given accuracy tolerance $\epsilon$. We also
propose a specific algorithm, namely a stochastic damped L-BFGS (SdLBFGS)
method, that falls under the proposed framework. {Moreover, we incorporate the
SVRG variance reduction technique into the proposed SdLBFGS method, and analyze
its SFO-calls complexity. Numerical results on a nonconvex binary
classification problem using SVM, and a multiclass classification problem using
neural networks are reported.
