  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 $O(\frac{1}{\sqrt{T}})$
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.
