Uniform Convergence of Sample Average Approximation with Adaptive Importance Sampling

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.


Technical Report IEMS Department Northwestern University, July 2015