A0435
Title: High-dimensional dynamic pricing under non-stationarity: Learning and earning with change-point detection
Authors: Zifeng Zhao - University of Notre Dame (United States) [presenting]
Abstract: A high-dimensional dynamic pricing problem is considered under non-stationarity, where a firm sells products to $T$ sequentially arriving consumers that behave according to an unknown demand model with potential changes. The demand model is a high-dimensional generalized linear model (GLM), allowing for a feature vector that encodes products and consumer information. To achieve optimal revenue (i.e., least regret), the firm needs to learn and exploit the unknown GLMs while monitoring for potential change points. First, a novel penalized likelihood-based online change-point detection algorithm is designed for high-dimensional GLMs, which is the first algorithm that achieves the optimal minimax localization error rate for high-dimensional GLMs. A change-point detection-assisted dynamic pricing (CPDP) policy is further proposed. It achieves a near-optimal regret of order $O(s\sqrt{\Upsilon_T T}\log(Td))$, where s is the sparsity level, and $\Upsilon_T$ is the number of change points. This regret is accompanied by a minimax lower bound, demonstrating the optimality of CPDP. In particular, the optimality concerning $\Upsilon_T$ 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 non-stationarity in dynamic pricing.
