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Experimental Results for Gradient Estimation and Optimization of a Markov Chain in Steady-State

  • Pierre L’Ecuyer
  • Nataly Giroux
  • Peter W. Glynn
Conference paper
  • 57 Downloads
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 374)

Abstract

Infinitesimal perturbation analysis (IPA) and the likelihood ratio (LR) method have drawn tots of attention recently, as ways of estimating the gradient of a performance measure with respect to continuous parameters in dynamic stochastic systems. In this paper, we experiment with the use of these estimators in stochastic approximation algorithms, to perform so-called “single-run optimizations” of steady-state systems, as suggested in [23]. We also compare them to finite-difference estimators, with and without common random numbers. In most cases, the simulation length must be increased from iteration to iteration, otherwise the algorithm converges to the wrong value. We have performed extensive numerical experiments with a simple M/M/1 queue. We state convergence results, but do not give the proofs. The proofs are given in [14].

Keywords

Service Time Busy Period Stochastic Approximation Gradient Estimator Dynamic Stochastic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Pierre L’Ecuyer
    • 1
  • Nataly Giroux
    • 2
  • Peter W. Glynn
    • 3
  1. 1.Département d’I.R.O.Université de MontréalMontréalCanada
  2. 2.Département d’informatiqueUniversité LavalSte-FoyCanada
  3. 3.Operations Research DepartmentStanford UniversityStanfordUSA

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