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