cs.LGFeb 18, 2026

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

Authors: Rachitesh Kumar, Omar Mouchtaki

Organizations: Carnegie Mellon University · New York University

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Abstract

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%.

Figures & tables

 Exploratory samples mm
Policy00112255
Kaplan–Meier0.0430.0430.0330.0330.0260.0260.0170.017
Our LP policy73.9%73.9\%53.7%53.7\%41.9%41.9\%60.1%60.1\%
Uncensored minimax lower bound22.3%22.3\%29.1%29.1\%36.6%36.6\%57.1%57.1\%
Table 1: Worst-case regret comparison at n=50n=50 , for the experimental setting in Section 5 . KM is reported in absolute terms; the other rows are percentages of KM. Entries are rounded from the computed regret bounds.
Figure 1: BSAA policy, q=0.8q=0.8 : effect of sample size nn .
Figure 2: KM policy, q=0.8q=0.8 : effect of sample size nn .
Figure 3: Worst-case regret at K=5K=5 censoring levels for different data-driven policies.
Figure 4: Certified worst-case regret bounds for LP-based policies and Kaplan–Meier, with the uncensored minimax lower bound at q=x=0.8q=x=0.8 and cu+co=1c_{u}+c_{o}=1 .
Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Figure 5: ΨkBSAA(t)\Psi^{\mathrm{BSAA}}_{k}(t) functions for K=5K=5 , q=0.9q=0.9 , and sample allocation n=(1,1,1,1,15)\bm{n}=(1,1,1,1,15) .
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