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

We present a self-contained proof of the convergence rate of the Stochastic Gradient Descent (SGD) when the learning rate follows an inverse time decays schedule; we next apply the results to the convergence of a modified form of policy gradient Multi-Armed Bandit (MAB) with $L2$ regularization.