  In this paper, we incorporate the Barzilai-Borwein step size into gradient
descent methods used to train deep networks. This allows us to adapt the
learning rate using a two-point approximation to the secant equation which
quasi-Newton methods are based upon. Moreover, the adaptive learning rate
method presented here is quite general in nature and can be applied to widely
used gradient descent approaches such as Adagrad and RMSprop. We evaluate our
method using standard example network architectures on widely available
datasets and compare against alternatives elsewhere in the literature. In our
experiments, our adaptive learning rate shows a smoother and faster convergence
than that exhibited by the alternatives, with better or comparable performance.
