  Progress in deep learning is slowed by the days or weeks it takes to train
large models. The natural solution of using more hardware is limited by
diminishing returns, and leads to inefficient use of additional resources. In
this paper, we present a large batch, stochastic optimization algorithm that is
both faster than widely used algorithms for fixed amounts of computation, and
also scales up substantially better as more computational resources become
available. Our algorithm implicitly computes the inverse Hessian of each
mini-batch to produce descent directions; we do so without either an explicit
approximation to the Hessian or Hessian-vector products. We demonstrate the
effectiveness of our algorithm by successfully training large ImageNet models
(Inception-V3, Resnet-50, Resnet-101 and Inception-Resnet-V2) with mini-batch
sizes of up to 32000 with no loss in validation error relative to current
baselines, and no increase in the total number of steps. At smaller mini-batch
sizes, our optimizer improves the validation error in these models by 0.8-0.9%.
Alternatively, we can trade off this accuracy to reduce the number of training
steps needed by roughly 10-30%. Our work is practical and easily usable by
others -- only one hyperparameter (learning rate) needs tuning, and
furthermore, the algorithm is as computationally cheap as the commonly used
Adam optimizer.
