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An Overview of Stochastic Approximation

In: Handbook of Simulation Optimization

Author

Listed:
  • Marie Chau

    (University of Maryland)

  • Michael C. Fu

    (University of Maryland)

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.

Suggested Citation

  • Marie Chau & Michael C. Fu, 2015. "An Overview of Stochastic Approximation," International Series in Operations Research & Management Science, in: Michael C Fu (ed.), Handbook of Simulation Optimization, edition 127, chapter 0, pages 149-178, Springer.
    • Handle: RePEc:spr:isochp:978-1-4939-1384-8_6
    DOI: 10.1007/978-1-4939-1384-8_6
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    Cited by:

    1. Eric Larsen & Sébastien Lachapelle & Yoshua Bengio & Emma Frejinger & Simon Lacoste-Julien & Andrea Lodi, 2022. "Predicting Tactical Solutions to Operational Planning Problems Under Imperfect Information," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 227-242, January.
    2. Tsai, Shing Chih & Yeh, Yingchieh & Kuo, Chen Yun, 2021. "Efficient optimization algorithms for surgical scheduling under uncertainty," European Journal of Operational Research, Elsevier, vol. 293(2), pages 579-593.
    3. David J. Eckman & Shane G. Henderson & Sara Shashaani, 2023. "Diagnostic Tools for Evaluating and Comparing Simulation-Optimization Algorithms," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 350-367, March.

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