What is the Value of Censored Data? An Exact Analysis for the Data-driven Newsvendor

2026-02-18

AI Summary

This work addresses the offline newsvendor problem under censored sales data—where only truncated observations, not true demand, are available—and proposes a general framework that transforms an infinite-dimensional nonconvex optimization into a tractable finite-dimensional problem. For the first time, it precisely characterizes the worst-case regret of classical inventory policies under arbitrary sample sizes and levels of censoring. The approach integrates Kaplan–Meier estimation, censored data analysis, and dimensionality reduction techniques in optimization, revealing that minimal, high-inventory-directed exploration can substantially improve performance. Theoretically, it demonstrates that the common “sales-as-demand” heuristic severely deteriorates under cumulative censoring, whereas policies incorporating directed exploration maintain near-optimal performance even in heavily censored regimes.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We study the offline data-driven newsvendor problem with censored demand data. In contrast to prior works where demand is fully observed, we consider the setting where demand is censored at the inventory level and only sales are observed; sales match demand when there is sufficient inventory, and equal the available inventory otherwise. We provide a general procedure to compute the exact worst-case regret of classical data-driven inventory policies, evaluated over all demand distributions. Our main technical result shows that this infinite-dimensional, non-convex optimization problem can be reduced to a finite-dimensional one, enabling an exact characterization of the performance of policies for any sample size and censoring levels. We leverage this reduction to derive sharp insights on the achievable performance of standard inventory policies under demand censoring. In particular, our analysis of the Kaplan-Meier policy shows that while demand censoring fundamentally limits what can be learned from passive sales data, just a small amount of targeted exploration at high inventory levels can substantially improve worst-case guarantees, enabling near-optimal performance even under heavy censoring. In contrast, when the point-of-sale system does not record stockout events and only reports realized sales, a natural and commonly used approach is to treat sales as demand. Our results show that policies based on this sales-as-demand heuristic can suffer severe performance degradation as censored data accumulates, highlighting how the quality of point-of-sale information critically shapes what can, and cannot, be learned offline.

Problem

• censored demand
• data-driven newsvendor
• sales-as-demand heuristic
• offline learning
• inventory policy

Innovation

• censored demand
• exact worst-case regret
• data-driven newsvendor
• Kaplan-Meier policy
• targeted exploration