Localized Exploration in Contextual Dynamic Pricing
We study the problem of contextual dynamic pricing with a linear demand model. We propose a novel localized exploration-then-commit (LetC) algorithm, which starts with a pure exploration stage, followed by a refinement stage that explores near the learned optimal pricing policy, and finally enters a pure exploitation stage. The algorithm is shown to achieve a minimax optimal, dimension-free regret bound when the time horizon exceeds a polynomial of the covariate dimension. Furthermore, we provide a general theoretical framework that encompasses the entire time spectrum, demonstrating how to balance exploration and exploitation when the horizon is limited. The analysis is powered by a novel critical inequality that depicts the exploration-exploitation trade-off in dynamic pricing, mirroring its existing counterpart for the bias-variance trade-off in regularized regression. Our theoretical results are validated by extensive experiments on synthetic and real-world data. (Joint work with Jinhang Chai, Yaqi Duan, and Kaizheng Wang)
Bio: Jianqing Fan is the Frederick L. Moore Professor at Princeton University. After receiving his Ph.D. from the University of California at Berkeley, he was appointed as assistant, associate, and full professor at the University of North Carolina at Chapel Hill, professor at the University of California at Los Angeles, professor and chair at Chinese University of Hong Kong. He was the past president of the Institute of Mathematical Statistics and the International Chinese Statistical Association. He is the joint editor of the Journal of the American Statistical Association and was the co-editor of The Annals of Statistics, Probability Theory and Related Fields, Econometrics Journal, Journal of Econometrics, and Journal of Business and Economics Statistics. His research interests include high-dimensional statistics, data science, machine learning, mathematics of AI, financial economics, and computational biology. He coauthored 4 books and published over 300 highly cited papers with a Google citation of 100,000. His published work has been recognized by The 2000 COPSS Presidents’ Award, Morningside Gold Medal of Applied Mathematics, Guggenheim Fellow, P.L. Hsu Prize, Guy medal in silver, Noether Distinguished Scholar Award, Le Cam Award and Lecture, Frontiers of Science Award, and Wald Memorial Award and Lecture, and election to Academician of Academia Sinica and Royal Academy of Belgium, and follow of American Associations for Advancement of Science, Institute of Mathematical Statistics, American Statistical Association, and Society of Financial Econometrics.