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Validating Sample Average Approximation Solutions with Negatively Dependent Batches

Jiajie Chen (chen***at***stat.wisc.edu)
Cong Han Lim (conghan***at***cs.wisc.edu)
Peter Qian (peterq***at***stat.wisc.edu)
Jeff Linderoth (linderoth***at***wisc.edu)
Stephen Wright (swright***at***cs.wisc.edu)

Abstract: Sample-average approximations (SAA) are a practical means of finding approximate solutions of stochastic programming problems involving an extremely large (or infinite) number of scenarios. SAA can also be used to find estimates of a lower bound on the optimal objective value of the true problem which, when coupled with an upper bound, provides confidence intervals for the true optimal objective value and valuable information about the quality of the approximate solutions. Specifically, the lower bound can be estimated by solving multiple SAA problems (each obtained using a particular sampling method) and averaging the obtained objective values. State-of-the-art methods for lower-bound estimation generate batches of scenarios for the SAA problems independently. In this paper, we describe sampling methods that produce negatively dependent batches, thus reducing the variance of the sample-averaged lower bound estimator and increasing its usefulness in defining a confidence interval for the optimal objective value. We provide conditions under which the new sampling methods can reduce the variance of the lower bound estimator, and present computational results to verify that our scheme can reduce the variance significantly, by comparison with the traditional Latin hypercube approach.

Keywords: Sample Average Approximation; Sampling; Latin Hypercube; Orthogonal Arrays

Category 1: Stochastic Programming


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Entry Submitted: 04/26/2014
Entry Accepted: 04/28/2014
Entry Last Modified: 02/15/2016

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