Temporal Fairness in Learning and Earning: Price Protection Guarantee and Phase Transitions
Prof. Ruihao Zhu
Assistant Professor of Operations, Technology, and Information Management
Cornell SC Johnson College of Business &
Nolan School of Hotel Administration
Motivated by the prevalence of “price protection guarantee”, which helps to promote temporal fairness in dynamic pricing, we study the impact of such policy on the design of online learning algorithm for data-driven dynamic pricing with initially unknown customer demand. Under the price protection guarantee, a customer who purchased a product in the past can receive a refund from the seller during the so-called price protection period (typically defined as a certain time window after the purchase date) in case the seller decides to lower the price. We consider a setting where a firm sells a product over a fixed time horizon and characterize how the length of price protection period can affect the optimal regret of the learning process. We first establish a fundamental impossible regime with a novel refund-aware regret lower bound analysis. Then, we propose LEAP, a phased exploration type algorithm for Learning and EArning under Price Protection to match this lower bound up to logarithmic factors or even doubly logarithmic factors (when there are only two prices available to the seller). Our results reveal the surprising phase transitions of the optimal regret with respect to the length of price protection period. Specifically, when this length is not too large, the optimal regret has no major difference when compared to that of the classic setting with no price protection guarantee. Moreover, there exists an upper limit on how much the optimal regret can deteriorate when this length of price protection period grows large. Finally, we conduct extensive numerical simulations with both synthetic and real-world datasets to show the benefit of LEAP over other heuristic methods for this problem.
Ruihao Zhu is currently an Assistant Professor at the Cornell University SC Johnson College of Business. He works on using machine learning and optimization to inform decision-making under uncertainty with applications in online platforms, revenue management, healthcare, and supply chain. Previously, he received his PhD degree from MIT and his bachelor degrees from the Shanghai Jiao Tong University and the University of Michigan.
