Before revision:  In this case, linear convergence rate of the expected function error is also proved , along with a worst-case \mathcal{O (\log(\varepsilon^{-1})) complexity bound} .  Numerical experiments, including comparisons with state-of-the art first- and second-order stochastic optimization methods, show the efficiency of our approach.
After revision:  In this case, linear convergence rate of the expected function error is also proved , along with a worst-case \mathcal{O (\log(\varepsilon^{-1})) complexity bound} . Numerical experiments, including comparisons with state-of-the art stochastic optimization methods, show the efficiency of our approach.