Global Stochastic Optimization with Low-Dispersion Point Sets

Sidney J. Yakowitz · Pierre L’Ecuyer · Felisa J. Vázquez-Abad

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Risk and Portfolio Optimization Stochastic Gradient Optimization Techniques Advanced Bandit Algorithms Research

Abstract

This study concerns a generic model-free stochastic optimization problem requiring the minimization of a risk function defined on a given bounded domain in a Euclidean space. Smoothness assumptions regarding the risk function are hypothesized, and members of the underlying space of probabilities are presumed subject to a large deviation principle; however, the risk function may well be nonconvex and multimodal. A general approach to finding the risk minimizer on the basis of decision/observation pairs is proposed. It consists of repeatedly observing pairs over a collection of design points. Principles are derived for choosing the number of these design points on the basis of an observation budget, and for allocating the observations between these points in both prescheduled and adaptive settings. On the basis of these principles, large-deviation type bounds of the minimizer in terms of sample size are established.

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References

1983Simulation Modeling and Analysis.1992Multivariate stochastic approximation using a simultaneous perturbation gradient approximation 1952Some aspects of the sequential design of experiments 1978Stochastic Approximation Methods for Constrained and Unconstrained Systems 1998Stochastic Approximation Algorithms and Applications 1991Gradient Estimation via Perturbation Analysis 1996Design and Analysis of Experiments for Statistical Selection, Screening and Multiple Comparisons 1994Simulation Modeling and Analysis (2nd Ed.)

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