论文标题
通过交易数据的上下文定价的凸面替代损失功能
Convex Surrogate Loss Functions for Contextual Pricing with Transaction Data
论文作者
论文摘要
我们研究了一个非政策的上下文定价问题,卖方可以访问以前提供的客户以前提供的价格样本,无论是以该价格购买的,以及描述客户和/或出售商品的辅助功能。这与研究良好的环境相反,在该环境中,观察到客户的估值样本(愿意支付的意愿)。在我们的环境中,观察到的数据受到以前的定价政策的影响,我们不知道客户将如何回应替代价格。我们为此设置介绍了合适的损失功能,可以直接优化,以找到具有预期收入保证的有效定价政策,而无需估算中间需求功能。我们专注于凸损失功能。当出于解释性原因而需要线性定价策略时,这尤其重要,从而导致可处理的凸收入优化问题。我们提出了广义铰链和分位定价损失函数,即以有条件的预期估值的乘法因素或出售价格的特定分数定价,尽管未观察到估值数据。当估值分布是对数符号时,我们分别证明了这些定价策略的预期收入范围,并为有限样本案例提供了概括性范围。最后,我们对合成和现实世界数据进行仿真,以证明这种方法具有竞争力,并且在某些情况下,在上下文定价中的最先进方法都超过了最先进的方法。
We study an off-policy contextual pricing problem where the seller has access to samples of prices that customers were previously offered, whether they purchased at that price, and auxiliary features describing the customer and/or item being sold. This is in contrast to the well-studied setting in which samples of the customer's valuation (willingness to pay) are observed. In our setting, the observed data is influenced by the previous pricing policy, and we do not know how customers would have responded to alternative prices. We introduce suitable loss functions for this setting that can be directly optimized to find an effective pricing policy with expected revenue guarantees, without the need for estimation of an intermediate demand function. We focus on convex loss functions. This is particularly relevant when linear pricing policies are desired for interpretability reasons, resulting in a tractable convex revenue optimization problem. We propose generalized hinge and quantile pricing loss functions that price at a multiplicative factor of the conditional expected valuation or a particular quantile of the prices that sold, despite the valuation data not being observed. We prove expected revenue bounds for these pricing policies respectively when the valuation distribution is log-concave, and we provide generalization bounds for the finite sample case. Finally, we conduct simulations on both synthetic and real-world data to demonstrate that this approach is competitive with, and in some settings outperforms, state-of-the-art methods in contextual pricing.