Accelerating Stochastic Composition Optimization

We consider the stochastic nested composition optimization problem where the objective is a composition of two expected-value functions. We propose a new stochastic first-order method, namely the accelerated stochastic compositional proximal gradient (ASC-PG) method. This algorithm updates the solution based on noisy gradient queries using a two-timescale iteration. The ASC-PG is the first proximal gradient method for the stochastic composition problem that can deal with nonsmooth regularization penalty. We show that the ASC-PG exhibits faster convergence than the best known algorithms, and that it achieves the optimal sample-error complexity in several important special cases. We demonstrate the application of ASC-PG to reinforcement learning and conduct numerical experiments.