Big Batch SGD: Automated Inference using Adaptive Batch Sizes

Classical stochastic gradient methods for optimization rely on noisy gradient approximations that become progressively less accurate as iterates approach a solution. The large noise and small signal in the resulting gradients makes it difficult to use them for adaptive stepsize selection and automatic stopping. We propose alternative “big batch” SGD schemes that adaptively grow the batch size over time to maintain a nearly constant signal-to-noise ratio in the gradient approximation. The resulting methods have similar convergence rates to classical SGD methods without requiring convexity of the objective function. The high fidelity gradients enable automated learning rate selection and do not require stepsize decay. For this reason, big batch methods are easily automated and can run with little or no user oversight.