Optimization applications often depend upon a huge number of uncertain parameters. In many contexts, however, the amount of relevant data per parameter is small, and hence, we may have only imprecise estimates. We term this setting -- where the number of uncertainties is large, but all estimates...

Motivated by the poor performance of cross-validation in settings where data are scarce, we propose a novel estimator of the out-of-sample performance of a policy in data-driven optimization. Our approach exploits the optimization problem's sensitivity analysis to estimate the gradient of the...