We study stochastic programs where the decision-maker cannot observe the
distribution of the exogenous uncertainties but has access to a finite set of
independent samples from this distribution. In this setting, the goal is to
find a procedure that transforms the data to an estimate of the expected cost
function under the unknown data-generating distribution, i.e., a predictor, and
an optimizer of the estimated cost function that serves as a near-optimal
candidate decision, i.e., a prescriptor. As functions of the data, predictors
and prescriptors constitute statistical estimators. We propose a
meta-optimization problem to find the least conservative predictors and
prescriptors subject to constraints on their out-of-sample disappointment. The
out-of-sample disappointment quantifies the probability that the actual
expected cost of the candidate decision under the unknown true distribution
exceeds its predicted cost. Leveraging tools from large deviations theory, we
prove that this meta-optimization problem admits a unique solution: The best
predictor-prescriptor pair is obtained by solving a distributionally robust
optimization problem over all distributions within a given relative entropy
distance from the empirical distribution of the data.

本文研究随机程序的优化问题，其中决策者不能观察到外生不确定性的分布，但可以访问此分布的有限样本。作者提出了一种元优化问题来找到最不保守的预测器和处方器，以及遵守它们的样本外失望约束。利用大偏差理论的工具，作者证明了该元优化问题有唯一解。最佳预测器 - 处方器对可以通过在距离数据的经验分布一定的相对熵距离内的所有分布上求解一个分布的鲁棒优化问题来获得。