用历史销售数据优化定价与库存，无需假设需求模型。
Nonparametric Contextual Pricing and Inventory Learning under Censored Demand
- 基于相似市场条件的历史数据，修复缺货导致的不完整销售信息。
- 在不依赖需求函数假设下实现最优学习速率，且平滑利润时更快收敛。
- 适合在线零售中需边服务边学习的动态定价与库存场景。
在线零售中，商品售罄时，商家仅能观测到实际售出数量，而无法得知若库存充足时有多少顾客会购买。库存水平决定了需求的可观测程度，这一信息会影响后续决策与未来收益。本文研究一种在线销售问题：每轮中，卖家观察市场背景后，基于之前轮次的被截断销售数据制定定价与补货策略。挑战在于，在不假设特定需求公式且无法观测真实利润的情况下学习上下文相关的定价与库存策略。为此，我们提出均值校准核上置信界（MCK-UCB）算法，将每次不完整的销售记录转化为对库存与价格决策的可靠指导，利用过去具有相似市场条件的数据。该设计使算法能在服务客户的同时学习，无需独立探索阶段，也无需还原因缺货而隐藏的需求。我们证明了该算法的极小极大最优性，当期望利润随价格变化更平滑时，收敛速度显著提升。大量数值实验验证了算法的有效性。
原文摘要 · Abstract (English)
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.
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