Stochastic Optimization via Grid Search
K. B. Ensor and P. W. Glynn
In Lectures in Applied Mathematics, Mathematics of Stochastic Manufacturing Systems Vol. 33, American Mathematical Society, [G.G. Yin, Q. Zhang, eds.], Providence, Rhode Island, 89 – 100 (1997)
This paper is concerned with the use of grid search as a means of optimizaing an objective function that can be evaluated only through simulation. We study the question of how rapidly the number of replications per grid point must grow relative to the number of grid points, in order to reduce the "noise" in the function evaluations and guarantee consistency. This question is studied in the context of Gaussian noise, stable noise, and noise having a finite moment generating function. We particularly focus on the limit behavior in the "critical case".