Normalized Direction-preserving Adam

Optimization algorithms for training deep models not only affects the convergence rate and stability of the training process, but are also highly related to the generalization performance of the models. While adaptive algorithms, such as Adam and RMSprop, have shown better optimization performance than stochastic gradient descent (SGD) in many scenarios, they often lead to worse generalization performance than SGD, when used for training deep neural networks (DNNs). In this work, we identify two problems of Adam that may degrade the generalization performance. As a solution, we propose the normalized direction-preserving Adam (ND-Adam) algorithm, which combines the best of both worlds, i.e., the good optimization performance of Adam, and the good generalization performance of SGD. In addition, we further improve the generalization performance in classification tasks, by using batch-normalized softmax. This study suggests the need for more precise control over the training process of DNNs.