High-Dimensional Dynamic Pricing Under Nonstationarity: Learning and Earning with Change-Point Detection

We consider a high-dimensional dynamic pricing problem under nonstationarity, in which a firm sells products to T sequentially arriving consumers that behave according to an unknown demand model with potential changes at unknown times. The demand model is assumed to be a high-dimensional generalized linear model (GLM), allowing for a feature vector in ${\mathbb{R}}^d$ that encodes products and consumer information. To achieve optimal revenue (i.e., least regret), the firm needs to learn and exploit the unknown GLMs, monitoring for potential change points. To tackle such a problem, we first design a novel penalized likelihood-based online change-point detection algorithm for high-dimensional GLMs, and this is the first algorithm in the change-point literature that achieves optimal minimax localization error rate for high-dimensional GLMs. A change-point detection assisted dynamic pricing (CPDP) policy is further proposed and achieves a near-optimal regret of order $O(s\sqrt{{\Upsilon }_{T}T}\hspace{0.17em}\log (Td))$, where s is the sparsity level and ${\Upsilon }_T$ is the number of change points. This regret is accompanied with a minimax lower bound, demonstrating the optimality of CPDP (up to logarithmic factors). In particular, the optimality with respect to ${\Upsilon }_T$ is seen for the first time in the dynamic pricing literature and is achieved via a novel accelerated exploration mechanism. Extensive simulation experiments and a real data application on online lending illustrate the efficiency of the proposed policy and the importance and practical value of handling nonstationarity in dynamic pricing.

This paper was accepted by Vivek Farias, data science.

Funding: F. Jiang is supported in part by the National Natural Science Foundation of China [Grants 72522009, 12201124, 12331009, 72271060, and 72432002] and National Key Research and Development Program of China [Grant 2024YFA1015700]. Y. Yu is supported by Engineering and Physical Sciences Research Council [Grant EP/Z531327/1] and the Leverhulme Trust.

Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.00889.