Limit Theorems for Simulation-Based Optimization via Random Search

This article develops fundamental theory related to the use of simulation-based nonadaptive random search as a means of optimizing a function that can be expressed as an expectation. Our results establish rates of convergence that express the trade-off between exploration and estimation, and fully characterize the limit distributions that arise. Our rates of convergence results should be viewed as a baseline against which to compare more intelligent algorithms.