Combining the Stochastic Counterpart and Stochastic ApproximationMethods

  • Authors:
  • Jean-Pierre Dussault;Donald Labrecque;Pierre L‘Ecuyer;Reuven Y. Rubinstein

  • Affiliations:
  • Département de mathématiques et informatique, Université de Sherbrooke, Sherbrooke J1K 2R1, Canada;Département d‘IRO, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal H3C 3J7, Canada;Département d‘IRO, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal H3C 3J7, Canada;Faculty of Industrial Engineering and Management Technion—Israel Institute of Technology, Haifa 32000, Israel and Department of Mathematics, EPFL-Ecublens CH-1015 Lausanne, Switzerland

  • Venue:
  • Discrete Event Dynamic Systems
  • Year:
  • 1997

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Abstract

In this work, we examine how to combine the score function methodwith the standard crude Monte Carlo and experimental design approaches,in order to evaluate the expected performance of a discrete eventsystem and its associated gradient simultaneously for differentscenarios (combinations of parameter values), as well as to optimizethe expected performance with respect to two parameter sets,which represent parameters of the underlying probability law(for the system‘s evolution) and parameters of the sample performancemeasure, respectively. We explore how the stochastic approximationand stochastic counterpart methods can be combined to performoptimization with respect to both sets of parameters at the sametime. We outline three combined algorithms of that form, onesequential and two parallel, and give a convergence proof forone of them. We discuss a number of issues related to the implementationand convergence of those algorithms, introduce averaging variants,and give numerical illustrations.