高维异质价格敏感多产品动态定价
Multi-Product Dynamic Pricing in High-Dimensions with Heterogeneous Price Sensitivity
摘要：
我们考虑的问题，多产品的动态定价，在上下文环境中，为卖方的差异化产品。在这种环境中，客户随着时间的推移而到达，产品由高维特征向量描述。每个客户根据广泛使用的多项Logit（MNL）选择模型选择产品，她的效用取决于产品的功能以及提供的价格。卖方先验不知道选择模型的参数，但可以通过与客户的互动来学习它们。卖方的目标是设计一个定价策略，最大限度地提高她的累积收入。这种模式受到Airbnb平台和在线广告等在线市场的推动。我们用后悔来衡量定价策略的表现，后悔是指对于预先知道选择模型参数并总是设定收入最大化价格的千里眼策略的预期收入损失。我们提出了一个定价策略，名为M3 P，实现了一个$T$ -周期遗憾$O(\log(Td) ( \sqrt{T}+ d\log(T)))$异构价格敏感性下的产品与尺寸$d$的功能。我们还使用信息理论的工具来证明，没有政策可以实现最坏情况下的$T$ -后悔比$Ω(\sqrt{T})$。
英文摘要：
We consider the problem of multi-product dynamic pricing, in a contextual setting, for a seller of differentiated products. In this environment, the customers arrive over time and products are described by high-dimensional feature vectors. Each customer chooses a product according to the widely used Multinomial Logit (MNL) choice model and her utility depends on the product features as well as the prices offered. The seller a-priori does not know the parameters of the choice model but can learn them through interactions with customers. The seller's goal is to design a pricing policy that maximizes her cumulative revenue. This model is motivated by online marketplaces such as Airbnb platform and online advertising. We measure the performance of a pricing policy in terms of regret, which is the expected revenue loss with respect to a clairvoyant policy that knows the parameters of the choice model in advance and always sets the revenue-maximizing prices. We propose a pricing policy, named M3P, that achieves a $T$-period regret of $O(\log(Td) ( \sqrt{T}+ d\log(T)))$ under heterogeneous price sensitivity for products with features of dimension $d$. We also use tools from information theory to prove that no policy can achieve worst-case $T$-regret better than $Ω(\sqrt{T})$.
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