In this paper we present a generic algorithmic framework, namely, the accelerated stochastic approximation (AC-SA) algorithm, for solving strongly convex stochastic composite optimization (SCO) problems. While the classical stochastic approximation (SA) algorithms are asymptotically optimal for solving differentiable and strongly convex problems, the AC-SA algorithm, when employed with proper stepsize policies, can achieve optimal or nearly optimal rates of convergence for solving different classes of SCO problems during a given number of iterations. Moreover, we investigate these AC-SA algorithms in more detail, such as, establishing the large-deviation results associated with the convergence rates and introducing efficient validation procedure to check the accuracy of the generated solutions.
Citation
Technical Report, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL.