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

2026-09-30

AI Summary

This study addresses the challenge of data-driven policy learning for multi-period inventory control with lost sales under censored demand. We propose a unified optimization framework that constructs covering conditions via cost decomposition techniques and introduces the first biased Sample Average Approximation (SAA) algorithm tailored for censored data, establishing both pessimistic and optimistic learning principles. By integrating base-stock policy analysis with exploration-exploitation mechanisms from reinforcement learning, the proposed algorithm achieves near-optimal sample complexity in offline settings and near-optimal cumulative regret bounds in online scenarios. Consequently, this work significantly enhances inventory decision quality under data-limited conditions.

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.

Problem

• Inventory Control
• Censored Demand
• Lost-sales
• Data-driven
• Multi-period

Innovation

• Censored Demand
• Biased Sample-Average Approximation
• Inventory Control
• Cost Decomposition
• Coverage Condition