Offline Feature-Based Pricing under Censored Demand: A Causal Inference Approach

Abstract

We study a feature-based pricing problem with demand censoring in an offline data-driven setting. In this problem, a firm is endowed with a finite amount of inventory, and faces a random demand that is dependent on the offered price and the covariates (from products, customers, or both). Any unsatisfied demand that exceeds the inventory level is lost and unobservable. The firm does not know the demand function but has access to an offline dataset consisting of quadruplets of historical covariates, inventory, price, and potentially censored sales quantity. Our objective is to use the offline dataset to find the optimal feature-based pricing rule so as to maximize the expected profit. Through the lens of causal inference, we propose a novel data-driven algorithm that is motivated by survival analysis and doubly robust estimation. We derive a finite sample regret bound to justify the proposed offline learning algorithm and prove its robustness. Extensive numerical experiments demonstrate the robust performance of our proposed algorithm in accurately estimating optimal prices on both training and testing data. Furthermore, these experiments highlight the value of considering demand censoring in the context of feature-based pricing.

Keywords: offline learning, feature-based pricing, demand censoring, causal inference, regret analysis