Uniform Convergence of Sample Average Approximation with Adaptive Importance Sampling

Published: 2015/07/23, Updated: 2017/04/10

Stochastic Programming adaptive importance sampling, adaptive multiple importance sampling, parametric integration, sample average approximation, uniform convergence Short URL: https://optimization-online.org/?p=13534

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.

Citation

Technical Report IEMS Department Northwestern University, July 2015