We consider dynamic pricing strategies in a streamed longitudinal data set-up where the objective is to maximize, over time, the cumulative profit across a large number of customer segments. We consider a dynamic model with the consumers' preferences as well as price sensitivity varying over time. Building on the well-known finding that consumers sharing similar characteristics act in similar ways, we consider a global shrinkage structure, which assumes that the consumers' preferences across the different segments can be well approximated by a spatial autoregressive (SAR) model. In such a streamed longitudinal set-up, we measure the performance of a dynamic pricing policy via regret, which is the expected revenue loss compared to a clairvoyant that knows the sequence of model parameters in advance. We propose a pricing policy based on penalized stochastic gradient descent (PSGD) and explicitly characterize its regret as functions of time, the temporal variability in the model parameters as well as the strength of the auto-correlation network structure spanning the varied customer segments. Our regret analysis results not only demonstrate asymptotic optimality of the proposed policy but also show that for policy planning it is essential to incorporate available structural information as policies based on unshrunken models are highly sub-optimal in the aforementioned set-up. We conduct simulation experiments across a wide range of regimes as well as real-world networks based studies and report encouraging performance for our proposed method.

翻译：我们考虑流式纵向数据设置下的动态定价策略，其目标是在时间维度上最大化大量客户细分群体的累计利润。我们采用了一个消费者偏好和价格敏感性随时间变化的动态模型。基于消费者具有相似特征会表现出相似行为的已知结论，我们引入了一种全局收缩结构，该结构假设不同细分群体的消费者偏好可通过空间自回归模型很好地近似。在此类流式纵向数据设置中，我们通过遗憾度量动态定价策略的性能，该遗憾定义为相较于预先知晓模型参数序列的全知者所获预期收入损失。我们提出了一种基于惩罚随机梯度下降的定价策略，并明确将其遗憾表征为时间、模型参数的时间变异性以及跨客户细分群体的自相关网络结构强度的函数。我们的遗憾分析结果不仅证明了所提策略的渐近最优性，还表明在策略规划中必须纳入可用的结构信息——因为基于非收缩模型的政策在上述设置下具有高度次优性。我们在广泛的不同场景以及现实网络数据上进行了仿真实验，结果表明我们的方法具有令人鼓舞的性能。