Distribution-free Contextual Dynamic Pricing
Distribution-free Contextual Dynamic Pricing
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DOI：
10.1287/moor.2023.1369
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发表时间：
2021-09
期刊：
影响因子：
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通讯作者：
Yiyun Luo;W. Sun;Yufeng Liu
中科院分区：
文献类型：
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作者：
Yiyun Luo;W. Sun;Yufeng Liu
上下文动态定价旨在根据与客户的顺序交互来设置个性化价格。每个时间段，都会有一位有兴趣购买产品的客户来到平台。客户对产品的评价是环境的线性函数，包括产品和客户特征，加上一些随机的市场噪音。卖家不会观察客户的真实估价，而是需要通过利用上下文信息和历史二进制购买反馈来了解估价。现有模型通常假设完全或部分了解随机噪声分布。在本文中，我们考虑线性估值模型中具有未知随机噪声的上下文动态定价。我们的无分配定价政策同时学习上下文功能和市场噪音。我们方法的一个关键要素是一种新颖的扰动线性老虎机框架，其中提出了一种改进的线性置信上限算法来平衡市场噪声的探索和利用当前知识以获得更好的定价。我们在扰动的线性老虎机框架中建立了策略的遗憾上限和匹配的下限，并证明了所考虑的定价问题中的次线性遗憾界限。最后，我们展示了我们的政策在模拟和现实汽车贷款数据集上的卓越性能。资助：Y. Liu 和 W.W. Sun 感谢美国国家科学基金会社会和经济科学部的支持 [Grant NSF-SES 2217440]。补充材料：补充材料可在 https://doi.org/10.1287/moor.2023.1369 获取。
Contextual dynamic pricing aims to set personalized prices based on sequential interactions with customers. At each time period, a customer who is interested in purchasing a product comes to the platform. The customer’s valuation for the product is a linear function of contexts, including product and customer features, plus some random market noise. The seller does not observe the customer’s true valuation, but instead needs to learn the valuation by leveraging contextual information and historic binary purchase feedback. Existing models typically assume full or partial knowledge of the random noise distribution. In this paper, we consider contextual dynamic pricing with unknown random noise in the linear valuation model. Our distribution-free pricing policy learns both the contextual function and the market noise simultaneously. A key ingredient of our method is a novel perturbed linear bandit framework, in which a modified linear upper confidence bound algorithm is proposed to balance the exploration of market noise and the exploitation of the current knowledge for better pricing. We establish the regret upper bound and a matching lower bound of our policy in the perturbed linear bandit framework and prove a sublinear regret bound in the considered pricing problem. Finally, we demonstrate the superior performance of our policy on simulations and a real-life auto loan data set. Funding: Y. Liu and W.W. Sun acknowledge support from the National Science Foundation Division of Social and Economic Sciences [Grant NSF-SES 2217440]. Supplemental Material: The supplementary material is available at https://doi.org/10.1287/moor.2023.1369 .