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Uniform Convergence of Sample Average Approximation with Adaptive Importance Sampling

Jeremy Staum (j-staum***at***northwestern.edu)
Andreas Waechter (waechter***at***iems.northwestern.edu)
Alvaro Maggiar (alvaro.maggiar***at***u.northwestern.edu)
Mingbin Feng (mingbinfeng2011***at***u.northwestern.edu)

Abstract: We study sample average approximations under adaptive importance sampling. Based on a Banach-space-valued martingale strong law of large numbers, we establish uniform convergence of the sample average approximation to the function being approximated. In the optimization context, we obtain convergence of the optimal value and optimal solutions of the sample average approximation.

Keywords: adaptive importance sampling, adaptive multiple importance sampling, sample average approximation, parametric integration, uniform convergence

Category 1: Stochastic Programming

Citation: Technical Report IEMS Department Northwestern University, July 2015

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Entry Submitted: 07/23/2015
Entry Accepted: 07/23/2015
Entry Last Modified: 04/10/2017

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