Stochastic Gradient Methods with Block Diagonal Matrix Adaptation

Adaptive gradient approaches that automatically adjust the learning rate on a per-feature basis have been very popular for training deep networks. This rich class of algorithms includes Adagrad, RMSprop, Adam, and recent extensions. All these algorithms have adopted diagonal matrix adaptation, due to the prohibitive computational burden of manipulating full matrices in high-dimensions. In this paper, we show that block-diagonal matrix adaptation can be a practical and powerful solution that can effectively utilize structural characteristics of deep learning architectures, and significantly improve convergence and out-of-sample generalization. We present a general framework with block-diagonal matrix updates via coordinate grouping, which includes counterparts of the aforementioned algorithms, prove their convergence in non-convex optimization, highlighting benefits compared to diagona