  The spectral gradient method is known to be a powerful low-cost tool for
solving large-scale optimization problems. In this paper, our goal is to
exploit its advantages in the stochastic optimization framework, especially in
the case of mini-batch subsampling that is often used in big data settings. To
allow the spectral coefficient to properly explore the underlying approximate
Hessian spectrum, we keep the same subsample for several iterations before
subsampling again. We analyze the required algorithmic features and the
conditions for almost sure convergence, and present initial numerical results
that show the advantages of the proposed method.
