面向需求截断下的最优库存控制：一种有偏样本平均近似方法

中文摘要 AI 辅助

我们研究了需求截断下的数据驱动多周期缺货库存控制问题，其中缺货仅揭示需求超过了库存水平。我们开发了一个统一的、基于模型的框架，用于从截断数据中进行策略学习，该框架基于对基础库存策略的新成本分解和有偏样本平均近似（SAA）方法。成本分解使我们能够提出一种新的覆盖条件，在该条件下，截断观测对于样本高效的策略学习具有足够的信息量。在此覆盖条件的指导下，我们设计了两种有偏SAA算法：一种上偏算法，在离线覆盖条件下实现接近最优的样本复杂度；另一种下偏算法，主动生成所需的覆盖，并在在线环境中实现接近最优的遗憾。更广泛地说，这种有偏SAA方法为在截断反馈下实施悲观和乐观提供了一般原则，这可能具有独立的研究价值。

英文摘要

We study data-driven multi-period lost-sales inventory control under censored demand, where a stockout reveals only that demand exceeded the stocking level. We develop a unified, model-based framework for policy learning from censored data, built on a new cost decomposition for base-stock policies and a biased sample-average approximation (SAA) approach. The cost decomposition allows us to propose a new coverage condition under which censored observations are informative enough for sample-efficient policy learning. Guided by this coverage condition, we design two biased SAA algorithms: an upper-biased one that achieves near-optimal sample complexity under the offline coverage condition, and a lower-biased one that actively generates the required coverage and achieves near-optimal regret online. More broadly, this biased SAA approach provides a general principle for implementing pessimism and optimism under censored feedback, which may be of independent interest.

发表机构

• Stern School of Business, New York University（纽约大学斯特恩商学院）

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