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We consider dynamic pricing strategies in a streamed longitudinal data set-upwhere the objective is to maximize, over time, the cumulative profit across alarge number of customer segments. We consider a dynamic model with theconsumers' preferences as well as price sensitivity varying over time. Buildingon the well-known finding that consumers sharing similar characteristics act insimilar ways, we consider a global shrinkage structure, which assumes that theconsumers' preferences across the different segments can be well approximatedby a spatial autoregressive (SAR) model. In such a streamed longitudinalset-up, we measure the performance of a dynamic pricing policy via regret,which is the expected revenue loss compared to a clairvoyant that knows thesequence of model parameters in advance. We propose a pricing policy based onpenalized stochastic gradient descent (PSGD) and explicitly characterize itsregret as functions of time, the temporal variability in the model parametersas well as the strength of the auto-correlation network structure spanning thevaried customer segments. Our regret analysis results not only demonstrateasymptotic optimality of the proposed policy but also show that for policyplanning it is essential to incorporate available structural information aspolicies based on unshrunken models are highly sub-optimal in theaforementioned set-up. We conduct simulation experiments across a wide range ofregimes as well as real-world networks based studies and report encouragingperformance for our proposed method.

Structured Dynamic Pricing: Optimal Regret in a Global Shrinkage Model