  Stochastic gradient algorithms have been the main focus of large-scale
learning problems and they led to important successes in machine learning. The
convergence of SGD depends on the careful choice of learning rate and the
amount of the noise in stochastic estimates of the gradients. In this paper, we
propose a new adaptive learning rate algorithm, which utilizes curvature
information for automatically tuning the learning rates. The information about
the element-wise curvature of the loss function is estimated from the local
statistics of the stochastic first order gradients. We further propose a new
variance reduction technique to speed up the convergence. In our preliminary
experiments with deep neural networks, we obtained better performance compared
to the popular stochastic gradient algorithms.
