An Overview of Stochastic Approximation

Marie Chau () and Michael C. Fu ()
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Marie Chau: University of Maryland
Michael C. Fu: University of Maryland

Chapter Chapter 6 in Handbook of Simulation Optimization, 2015, pp 149-178 from Springer

Abstract: Abstract This chapter provides an overview of stochastic approximation (SA) methods in the context of simulation optimization. SA is an iterative search algorithm that can be viewed as the stochastic counterpart to steepest descent in deterministic optimization. We begin with the classical methods of Robbins–Monro (RM) and Kiefer–Wolfowitz (KW). We discuss the challenges in implementing SA algorithms and present some of the most well-known variants such as Kesten’s rule, iterate averaging, varying bounds, and simultaneous perturbation stochastic approximation (SPSA), as well as recently proposed versions including scaled-and-shifted Kiefer–Wolfowitz (SSKW), robust stochastic approximation (RSA), accelerated stochastic approximation (AC-SA) for convex and strongly convex functions, and Secant-Tangents AveRaged stochastic approximation (STAR-SA). We investigate the empirical performance of several of the recent algorithms by comparing them on a set of numerical examples.

Keywords: Feasible Region; Stochastic Approximation; Simulation Optimization; Simultaneous Perturbation Stochastic Approximation; Stochastic Approximation Algorithm (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-1-4939-1384-8_6

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