A New Accelerated Stochastic Gradient Method with Momentum.

In this paper, we propose a novel accelerated stochastic gradient method with momentum, which momentum is the weighted average of previous gradients. The weights decays inverse proportionally with the iteration times. Stochastic gradient descent with momentum (Sgdm) use weights that decays exponentially with the iteration times to generate an momentum term. Using exponentially decaying weights, variants of Sgdm with well designed and complicated formats have been proposed to achieve better performance. The momentum update rules of our method is as simple as that of Sgdm. We provide theoretical convergence properties analyses for our method, which show both the exponentially decay weights and our inverse proportionally decay weights can limit the variance of the moving direction of parameters to be optimized to a region. Experimental results empirically show that our method works well with practical problems and outperforms Sgdm, and it outperforms Adam in convolutional neural networks.