Towards Optimal Inventory Control under Censored Demand: A Biased Sample-Average Approximation Approach

Abstract: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.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2609.39397 [stat.ML]

(or arXiv:2609.39397v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2609.39397 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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