Offline Pricing and Demand Learning with Censored Data

We study a single product pricing problem with demand censoring in an offline data-driven setting. In this problem, retailer has finite amount of inventory and faces random that is price sensitive linear fashion unknown sensitivity base distribution. Any unsatisfied exceeds the level lost unobservable. assume access to data set consisting triples historical price, level, potentially censored sales quantity. The retailer’s objective use find optimal maximizing his or her expected revenue inventories. Because data, we show existence near-optimal algorithms problem—which call identifiability—is not always guaranteed. develop necessary sufficient condition for identifiability by comparing solutions two distributionally robust optimization problems. propose novel algorithm hedges against distributional uncertainty arising from provable finite-sample performance guarantees regardless quality. Specifically, prove that, identifiable problems, proposed and, unidentifiable its worst-case loss approaches best-achievable minimax any must incur. Numerical experiments demonstrate our highly effective significantly improves both revenues compared three regression-based algorithms. This paper was accepted J. George Shanthikumar, big analytics. Funding: work supported MIT Data Science Laboratory. Bu partially Hong Kong Polytechnic University Start-up Fund New Recruits [Project ID P0039585]. Supplemental Material: online appendices are available at https://doi.org/10.1287/mnsc.2022.4382 .