Stochastic Gradient Decent (SGD) is one of the core techniques behind the success of deep neural networks. The gradient provides information on the direction in which function has the steepest rate of change. The main problem with basic SGD is to change by equal sized steps for all parameters, irrespective of gradient behavior. Hence, an efficient way of deep network optimization is to make adaptive step sizes for each parameter. Recently, several attempts have been made to improve gradient descent methods such as AdaGrad, AdaDelta, RMSProp and Adam. These methods rely on the square roots of exponential moving averages of squared past gradients. Thus, these methods do not take the advantage of local change in gradients. In this paper, a novel optimizer is proposed based on the difference between the present and the immediate past gradient (i.e., diffGrad). In the proposed diffGrad optimization technique, the step size is adjusted for each parameter in such a way that it should have a larger step size for faster gradient changing parameters and lower step size for lower gradient changing parameters. The convergence analysis is done using the regret bound approach of online learning framework. Rigorous analysis is made in this paper over three synthetic complex non-convex functions. The image categorization experiments are also conducted over the CIFAR10 and CIFAR100 datasets to observe the performance of diffGrad with respect to the state-of-the-art optimizers such as SGDM, AdaGrad, AdaDelta, RMSProp, AMSGrad, and Adam. The residual unit (ResNet) based Convolutional Neural Networks (CNN) architecture is used in the experiments. The experiments show that diffGrad outperforms the other optimizers. Also, we showed that diffGrad performs uniformly well on network using different activation functions. The source code is made publicly available at https://github.com/shivram1987/diffGrad.

本文提出了一种新的优化器 diffGrad，它基于当前和上一梯度之间的差异，并根据参数的梯度变化速度动态调整步长。作者通过实验证明了 diffGrad 在图像分类等任务上的优越性能，特别是与其他优化器相比，diffGrad 对于使用不同激活函数的 CNN 训练具有一致的优越表现。

diffGrad: 卷积神经网络的一种优化方法