When using large-batch training to speed up stochastic gradient descent, learning rates must adapt to new batch sizes in order to maximize speed-ups and preserve model quality. Re-tuning learning rates is resource intensive, while fixed scaling rules often degrade model quality. We propose AdaScale SGD, an algorithm that reliably adapts learning rates to large-batch training. By continually adapting to the gradients variance, AdaScale automatically achieves speed-ups for a wide range of batch sizes. We formally describe this quality with AdaScales convergence bound, which maintains final objective values, even as batch sizes grow large and the number of iterations decreases. In empirical comparisons, AdaScale trains well beyond the batch size limits of popular linear learning rate scaling rules. This includes large-batch training with no model degradation for machine translation, image classification, object detection, and speech recognition tasks. AdaScales qualitative behavior is similar to that of warm-up heuristics, but unlike warm-up, this behavior emerges naturally from a principled mechanism. The algorithm introduces negligible computational overhead and no new hyperparameters, making AdaScale an attractive choice for large-scale training in practice.