Metric Entropy and Nonasymptotic Confidence Bands in Stochastic Programming
Abstract
Talagrand has demonstrated in his key paper, how the metric entropy of a class of functions relates to uniform bounds for the law of large numbers. This paper shows how to calculate the metric entropy of classes of functions which appear in stochastic optimization problems. As a consequence of these results, we derive via variational inequalities confidence bands for the solutions, which are valid for any sample size. In particular, the linear recourse problem is considered.