On the Convergence Rate of the Stochastic Gradient Descent (SGD) and application to a modified policy gradient for the Multi Armed Bandit

The Stochastic Gradient Descent (SGD) is extensively used in Deep Learning (see [2]). A direct and simple proof of a convergence result of the SGD is given in [3]. Here we will go further and investigate the convergence rate of the SGD, giving some elementary proofs, for two choices of the "learning rate", both in the class of'inverse time decay' schedules.