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, a retailer has a finite amount of inventory and faces a random demand that is price sensitive in a linear fashion with unknown price sensitivity and base demand distribution. Any unsatisfied demand that exceeds the inventory level is lost and unobservable. We assume that the retailer has access to an offline data set consisting of triples of historical price, inventory level, and potentially censored sales quantity. The retailer’s objective is to use the offline data set to find an optimal price, maximizing his or her expected revenue with finite inventories. Because of demand censoring in the offline data, we show that the existence of near-optimal algorithms in a data-driven problem—which we call problem identifiability— is not always guaranteed. We develop a necessary and sufficient condition for problem identifiability by comparing the solutions to two distributionally robust optimization problems. We propose a novel data-driven algorithm that hedges against the distributional uncertainty arising from censored data, with provable finite-sample performance guarantees regardless of problem identifiability and offline data quality. Specifically, we prove that, for identifiable problems, the proposed algorithm is near-optimal and, for unidentifiable problems, its worst-case revenue loss approaches the best-achievable minimax revenue loss that any data-driven algorithm must incur. Numerical experiments demonstrate that our proposed algorithm is highly effective and significantly improves both the expected and worst-case revenues compared with three regression-based algorithms.