We study a censored variant of the data-driven newsvendor problem, where the decision-maker must select an ordering quantity that minimizes expected overage and underage costs based only on offline censored sales data, rather than historical demand realizations. Our goal is to understand how the degree of historical demand censoring affects the performance of any learning algorithm for this problem. To isolate this impact, we adopt a distributionally robust optimization framework, evaluating policies according to their worst-case regret over an ambiguity set of distributions. This set is defined by the largest historical order quantity (the observable boundary of the dataset), and contains all distributions matching the true demand distribution up to this boundary, while allowing them to be arbitrary afterwards. We demonstrate a spectrum of achievability under demand censoring by deriving a natural necessary and sufficient condition under which vanishing regret is an achievable goal. In regimes in which it is not, we exactly characterize the information loss due to censoring: an insurmountable lower bound on the performance of any policy, even when the decision-maker has access to infinitely many demand samples. We then leverage these sharp characterizations to propose a natural robust algorithm that adapts to the historical level of demand censoring. We derive finite-sample guarantees for this algorithm across all possible censoring regimes and show its near-optimality with matching lower bounds (up to polylogarithmic factors). We moreover demonstrate its robust performance via extensive numerical experiments on both synthetic and real-world datasets.

翻译：我们研究数据驱动报童问题的一个删失变体，其中决策者必须仅基于离线删失销售数据（而非历史需求实现值）选择最小化预期超储与缺货成本的订购量。我们的目标是理解历史需求删失程度如何影响针对该问题的任何学习算法的性能。为分离这种影响，我们采用分布鲁棒优化框架，根据策略在模糊分布集上的最坏情况遗憾来评估其性能。该集合由最大历史订购量（数据集的可观测边界）定义，包含所有在此边界之前与真实需求分布匹配的分布，同时允许这些分布在此边界之后任意变化。通过推导一个自然且充分必要的条件，我们证明了在需求删失下可实现性的连续谱，其中渐近消失的遗憾是可实现的目标。在不可实现的机制中，我们精确刻画了由删失导致的信息损失：这是任何策略性能的不可逾越下界，即使决策者能够获取无限多的需求样本。随后，我们利用这些精确刻画提出一种自然的鲁棒算法，该算法能自适应历史需求删失水平。我们为该算法在所有可能的删失机制下推导了有限样本保证，并通过匹配下界（至多差多对数因子）证明了其近乎最优性。此外，我们通过在合成和真实世界数据集上的大量数值实验验证了其鲁棒性能。