High-Dimensional Dynamic Pricing under Non-Stationarity: Learning and Earning with Change-Point Detection

We consider a high-dimensional dynamic pricing problem under non-stationarity, where 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 Rd 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. To tackle such a problem, we first design a novel penalized likelihood-based online change-point detection algorithm for high-dimensional GLMs, which 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√UpsilonT Tlog(Td)), where s is the sparsity level and UpsilonT 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 UpsilonT 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.