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Sample Average Approximation with Adaptive Importance Sampling

Andreas Waechter (andreas.waechter***at***northwestern.edu)
Jeremy Staum (j-staum***at***northwestern.edu)
Alvaro Maggiar (alvaro.maggiar***at***u.northwestern.edu)
Mingbin Feng (ben.feng***at***uwaterloo.ca)

Abstract: We study sample average approximations under adaptive importance sampling in which the sample densities may depend on previous random samples. Based on a generic uniform law of large numbers, we establish uniform convergence of the sample average approximation to the true function. We obtain convergence of the optimal value and optimal solutions of the sample average approximation. The relevance of this result is demonstrated in the context of the convergence analysis of a randomized optimization algorithm.

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

Category 1: Stochastic Programming

Citation: Technical Report IEMS Department Northwestern University, October 2017

Download: [PDF]

Entry Submitted: 04/07/2017
Entry Accepted: 04/08/2017
Entry Last Modified: 11/13/2017

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