Nonparametric Contextual Pricing and Inventory Learning under Censored Demand
2026-08-31 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study how online sellers can set prices and decide stock levels when they only see how many products actually sold, not how many customers wanted them but found the item sold out. They create an algorithm called MCK-UCB that learns good pricing and stocking strategies using past sales data from similar situations, without needing to guess the exact demand or separate learning from selling time. Their method improves over time and can handle cases where demand changes smoothly with price. They prove their approach is mathematically optimal and test it thoroughly to show it works well.
online retailingpricing strategyinventory managementdemand censorshipmulti-armed banditkernel methodsUCB algorithmminimax optimalitycontextual learningexploration-exploitation tradeoff
Authors
Zean Han, Jing Liang, Ruihan Lin, Zezhen Ding, Jiheng Zhang
Abstract
In online retailing, when a product sells out, a retailer often sees only the units sold, not how many customers would have bought it had inventory been available. However, the inventory level determines how much demand is revealed, and this information can influence subsequent decisions and future profits. We study an online selling problem in which, in each round, the seller observes a market context and then makes pricing and stocking decisions based on censored sales data from previous rounds. The challenge is to learn a context-dependent pricing and stocking policy without assuming a particular formula for demand or observing realized profit. To overcome this difficulty, we propose a Mean-Calibrated Kernel UCB (MCK-UCB) algorithm that turns each incomplete sales record into a reliable guide for both inventory and price decisions, using data from past rounds with similar market conditions. This design allows us to learn while serving customers, without a separate exploration phase or the need to recover all demand hidden by stockouts. We prove the minimax optimality of the proposed algorithm, with strictly faster rates when expected profit varies more smoothly with price. Comprehensive numerical experiments have been conducted to confirm the effectiveness of the proposed algorithm.