Title: Admissibility of solution estimators for stochastic optimization,
Abstract: We look at stochastic optimization problems through the lens of statistical
decision theory. In particular, we address admissibility, in the statistical
decision theory sense, of the natural sample average estimator for a stochastic
optimization problem (which is also known as the empirical risk minimization
(ERM) rule in learning literature). It is well known that for general
stochastic optimization problems, the sample average estimator may not be
admissible. This is known as Stein's paradox in the statistics literature. We
show in this paper that for optimizing stochastic linear functions over compact
sets, the sample average estimator is admissible.