In the Newsvendor problem, the goal is to guess the number that will be drawn from some distribution, with asymmetric consequences for guessing too high vs. too low. In the data-driven version, the distribution is unknown, and one must work with samples from the distribution. Data-driven Newsvendor has been studied under many variants: additive vs. multiplicative regret, high probability vs. expectation bounds, and different distribution classes. This paper studies all combinations of these variants, filling in many gaps in the literature and simplifying many proofs. In particular, we provide a unified analysis based on the notion of clustered distributions, which in conjunction with our new lower bounds, shows that the entire spectrum of regrets between $1/\sqrt{n}$ and $1/n$ can be possible. Simulations on commonly-used distributions demonstrate that our notion is the "correct" predictor of empirical regret across varying data sizes.

翻译：在报童问题中，目标是从某个分布中猜测将被抽取的数量，其中猜测过高与过低的结果具有非对称性。在数据驱动版本中，分布是未知的，必须基于分布样本进行决策。数据驱动报童问题已在多种变体下得到研究：加性与乘性遗憾、高概率与期望界，以及不同的分布类别。本文研究了这些变体的所有组合，填补了文献中的诸多空白并简化了众多证明。特别地，我们基于聚类分布的概念提出了统一分析框架，结合我们提出的新下界，表明在 $1/\sqrt{n}$ 到 $1/n$ 之间的完整遗憾谱系均可能实现。在常用分布上的仿真实验表明，我们的概念是跨不同数据规模时经验遗憾的"正确"预测指标。