New logarithmic step size for stochastic gradient descent

In this paper, we propose a novel warm restart technique using a new logarithmic step size for the stochastic gradient descent (SGD) approach. For smooth and non-convex functions, we establish an \(O\left(1\over{\sqrt{T}}\right)\) $$O\left(\frac{1}{\sqrt{T}}\right)$$ convergence rate for the SGD. We conduct a comprehensive implementation to demonstrate the efficiency of the newly proposed step size on the FashionMinst, CIFAR10, and CIFAR100 datasets. Moreover, we compare our results with nine other existing approaches and demonstrate that the new logarithmic step size improves test accuracy by 0.9% for the CIFAR100 dataset when we utilize a convolutional neural network (CNN) model.