Personalized Dynamic Pricing with Machine Learning: High Dimensional Features and Heterogeneous Elasticity
Résumé
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, i.e., the revenue loss against a clairvoyant who knows the underlying demand relationship, is at least of order \(s\sqrt{T}\)% under any admissible policy. We then design a near-optimal pricing policy for a “semi-clairvoyant” seller (who knows which \(s\) of the \(d\) features are in the demand model) that achieves an expected regret of order \(s\sqrt{T}\log T\). 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 \(s\sqrt{T} (\log d＋\log T)\), 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.
Biographie
Dr. Gah-Yi Ban est professeur agrégée à l’école de gestion de Imperial College à Londres et anciennement de la London Business School et de l’Université du Maryland. Elle détient un doctorat en recherche opérationnelle de l’Université de Californie à Berkeley (UCB) et sert en qualité de rédactrice ajointe de Management Science, M&SOM et de Operations Research Letter. Ses intérêts de recherche sont en analytique des mégadonnées, plus spécialement la prise de décision dans des environnements incertains en haute-dimension avec des applications en gestion. Ses recherches ont été couronnées du prix Best OM Paper in Operations Research award en 2021.