We study a pricing setting where each customer is offered a contextualized price based on customer and/or product features. Often only historical sales data are available, so we observe whether a customer purchased a product at the price prescribed rather than the customer's true valuation. Such observational data are influenced by historical pricing policies, which introduce difficulties in evaluating the effectiveness of future policies. The goal of this paper is to formulate loss functions that can be used for evaluating pricing policies directly from observational data, rather than going through an intermediate demand estimation stage, which may suffer from bias. To achieve this, we adapt ideas from machine learning with corrupted labels, where we consider each observed purchase decision as a known probabilistic transformation of the customer's valuation. From this transformation, we derive a class of unbiased loss functions. Within this class, we identify minimum variance estimators and estimators robust to poor demand estimation. Furthermore, we show that for contextual pricing, estimators popular in the off-policy evaluation literature fall within this class of loss functions. We offer managerial insights into scenarios under which these estimators are effective.

翻译：我们研究一个定价设置,向每个客户提供基于客户和(或)产品特点的背景价格。通常只有历史销售数据,因此我们观察客户是否以规定的价格而不是客户的真正估值购买产品。这种观察数据受历史定价政策的影响,这些政策在评估未来政策的有效性方面造成困难。本文的目的是制定损失功能,直接从观察数据中直接用来评价定价政策,而不是通过中间需求估计阶段,这可能受到偏见的影响。为了实现这一点,我们调整了机器学习腐败标签后的想法,我们认为每个观察到的购买决定都是已知的客户估值概率变换。我们从这一转变中得出了一个不偏颇的损失功能类别。在这个类别中,我们确定最小的差异估计者和估算者,对需求估计力不强。此外,我们显示,在背景定价方面,非政策评价文献中受欢迎的估计者属于这一损失类别的职能。我们从管理角度深入了解这些估计者是否有效的情景。