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Sample-average approximations (SAA) are a practical means of findingapproximate solutions of stochastic programming problems involving an extremelylarge (or infinite) number of scenarios. SAA can also be used to find estimatesof a lower bound on the optimal objective value of the true problem which, whencoupled with an upper bound, provides confidence intervals for the true optimalobjective value and valuable information about the quality of the approximatesolutions. Specifically, the lower bound can be estimated by solving multipleSAA problems (each obtained using a particular sampling method) and averagingthe obtained objective values. State-of-the-art methods for lower-boundestimation generate batches of scenarios for the SAA problems independently. Inthis paper, we describe sampling methods that produce negatively dependentbatches, thus reducing the variance of the sample-averaged lower boundestimator and increasing its usefulness in defining a confidence interval forthe optimal objective value. We provide conditions under which the new samplingmethods can reduce the variance of the lower bound estimator, and presentcomputational results to verify that our scheme can reduce the variancesignificantly, by comparison with the traditional Latin hypercube approach.

Validating Sample Average Approximation Solutions with Negatively Dependent Batches