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Accelerating Stochastic Composition Optimization

Mengdi Wang, Ji Liu, Ethan X. Fang; 18(105):1−23, 2017.

Abstract

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.

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