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

We study the offline data-driven newsvendor problem when historical demand is censored by past inventory levels. We introduce a class of policies for which worst-case expected regret over all bounded demand distributions admits an exact finite-dimensional characterization, valid for any sample size and historical inventory design. The dimension depends on the number of distinct inventory levels, rather than the number of observations. This framework yields exact analyses of the sales-as-demand heuristic, the Kaplan-Meier policy, and recent policies from the censored-newsvendor literature. 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. Finally, we further leverage our reduction to design new policies that push the frontier and substantially improve upon the worst-case regret of known policies, reducing it by up to 40%.