Stochastic Gradient Descent, Weighted Sampling, and the Randomized Kaczmarz algorithm

We improve a recent gurantee of Bach and Moulines on the linear convergence of SGD for smooth and strongly convex objectives, reducing a quadratic dependence on the strong convexity to a linear dependence. Furthermore, we show how reweighting the sampling distribution (i.e. Our results are based on a connection we make between SGD and the randomized Kaczmarz algorithm, which allows us to transfer ideas between the separate bodies of literature studying each of the two methods.