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Stochastic Gradient Estimation

In: Handbook of Simulation Optimization

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  • Michael C. Fu

    (University of Maryland)

Abstract

This chapter reviews simulation-based methods for estimating gradients, which are central to gradient-based simulation optimization algorithms such as stochastic approximation and sample average approximation. We begin by describing approaches based on finite differences, including the simultaneous perturbation method. The remainder of the chapter then focuses on the direct gradient estimation techniques of perturbation analysis, the likelihood ratio/score function method, and the use of weak derivatives (also known as measure-valued differentiation). Various examples are provided to illustrate the different estimators—for a single random variable, a stochastic activity network, and a single-server queue. Recent work on quantile sensitivity estimation is summarized, and several newly proposed approaches for using stochastic gradients in simulation optimization are discussed.

Suggested Citation

  • Michael C. Fu, 2015. "Stochastic Gradient Estimation," International Series in Operations Research & Management Science, in: Michael C Fu (ed.), Handbook of Simulation Optimization, edition 127, chapter 0, pages 105-147, Springer.
    • Handle: RePEc:spr:isochp:978-1-4939-1384-8_5
    DOI: 10.1007/978-1-4939-1384-8_5
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    Citations

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    Cited by:

    1. Huashuai Qu & Ilya O. Ryzhov & Michael C. Fu & Eric Bergerson & Megan Kurka & Ludek Kopacek, 2020. "Learning Demand Curves in B2B Pricing: A New Framework and Case Study," Production and Operations Management, Production and Operations Management Society, vol. 29(5), pages 1287-1306, May.
    2. L. Jeff Hong & Guangxin Jiang, 2019. "Offline Simulation Online Application: A New Framework of Simulation-Based Decision Making," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(06), pages 1-22, December.
    3. Zhenyu Cui & Michael C. Fu & Jian-Qiang Hu & Yanchu Liu & Yijie Peng & Lingjiong Zhu, 2020. "On the Variance of Single-Run Unbiased Stochastic Derivative Estimators," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 390-407, April.
    4. Joost Berkhout & Bernd Heidergott & Henry Lam & Yijie Peng, 2019. "From Data to Stochastic Modeling and Decision Making: What Can We Do Better?," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(06), pages 1-20, December.
    5. Yijie Peng & Michael C. Fu & Bernd Heidergott & Henry Lam, 2020. "Maximum Likelihood Estimation by Monte Carlo Simulation: Toward Data-Driven Stochastic Modeling," Operations Research, INFORMS, vol. 68(6), pages 1896-1912, November.
    6. Shi Pu & Alfredo Garcia, 2018. "A Flocking-Based Approach for Distributed Stochastic Optimization," Operations Research, INFORMS, vol. 66(1), pages 267-281, January.

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