Personalized Dynamic Pricing with Machine Learning: High-Dimensional Features and Heterogeneous Elasticity

We consider a seller who can dynamically adjust the price of a product at the individual customer level, by utilizing information about customers’ characteristics encoded as a d -dimensional feature vector. We assume a personalized demand model, parameters of which depend on s out of the d features. The seller initially does not know the relationship between the customer features and the product demand but learns this through sales observations over a selling horizon of T periods. We prove that the seller’s expected regret, that is, the revenue loss against a clairvoyant who knows the underlying demand relationship, is at least of order s T under any admissible policy. We then design a near-optimal pricing policy for a semiclairvoyant seller (who knows which s of the d features are in the demand model) who achieves an expected regret of order s T log T . We extend this policy to a more realistic setting, where the seller does not know the true demand predictors, and show that this policy has an expected regret of order s T ( log d + log T ) , which is also near-optimal. Finally, we test our theory on simulated data and on a data set from an online auto loan company in the United States. On both data sets, our experimentation-based pricing policy is superior to intuitive and/or widely-practiced customized pricing methods, such as myopic pricing and segment-then-optimize policies. Furthermore, our policy improves upon the loan company’s historical pricing decisions by 47% in expected revenue over a six-month period.