Statistical inference of multistage stochastic programming problems

Alexander Shapiro (ashapiroisye.isye.gatech.edu)

Abstract: We discuss in this paper statistical inference of sample average approximations of multistage stochastic programming problems. We show that any random sampling scheme provides a valid statistical lower bound for the optimal value of the true problem. However, in order for such lower bound to be consistent one needs to employ the conditional sampling procedure. We also indicate that fixing a feasible first-stage solution and then solving the sampling approximation of the corresponding minus-one-stage problem, does not give a valid statistical upper bound for the optimal value of the true problem.

Keywords: stochastic programming, multistage stochastic programs with recourse, Monte Carlo sampling, statistical bounds, consistent estimators

Category 1: Stochastic Programming

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Entry Submitted: 01/18/2002
Entry Accepted: 01/18/2002
Entry Last Modified: 01/18/2002

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