Variable-sample methods for stochastic optimization

Tito Homem-De-Mello
2003 ACM Transactions on Modeling and Computer Simulation  
In this article we discuss the application of a certain class of Monte Carlo methods to stochastic optimization problems. Particularly, we study variable-sample techniques, in which the objective function is replaced, at each iteration, by a sample average approximation. We first provide general results on the schedule of sample sizes, under which variable-sample methods yield consistent estimators as well as bounds on the estimation error. Because the convergence analysis is performed
more » ... performed pathwisely, we are able to obtain our results in a flexible setting, which requires mild assumptions on the distributions and which includes the possibility of using different sampling distributions along the algorithm. We illustrate these ideas by studying a modification of the well-known pure random search method, adapting it to the variable-sample scheme, and show conditions for convergence of the algorithm. Implementation issues are discussed and numerical results are presented to illustrate the ideas.
doi:10.1145/858481.858483 fatcat:injtu5lbszhijkslxomugka4jm