Meta Dynamic Pricing: Transfer Learning Across Experiments

• 成果类型: Article
• 署名作者: Bastani, Hamsa; Simchi-Levi, David; Zhu, Ruihao
• 署名单位: University of Pennsylvania; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Purdue University System; Purdue University
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2021.4071
• 发表日期: 2022
• 页码: 1865-1881
• 关键词: Thompson sampling; misspecified prior; Transfer Learning; meta learning; EMPIRICAL BAYES

摘要

We study the problem of learning shared structure across a sequence of dynamic pricing experiments for related products. We consider a practical formulation in which the unknown demand parameters for each product come from an unknown distribution (prior) that is shared across products. We then propose a meta dynamic pricing algorithm that learns this prior online while solving a sequence of Thompson sampling pricing experiments (each with horizon T) for N different products. Our algorithm addresses two challenges: (i) balancing the need to learn the prior (meta-exploration) with the need to leverage the estimated prior to achieve good performance (meta-exploitation) and (ii) accounting for uncertainty in the estimated prior by appropriately widening the estimated prior as a function of its estimation error. We introduce a novel prior alignment technique to analyze the regret of Thompson sampling with a misspecified prior, which may be of independent interest. Unlike prior-independent approaches, our algorithm's meta regret grows sublinearly in N, demonstrating that the price of an unknown prior in Thompson sampling can be negligible in experiment-rich environments (large N). Numerical experiments on synthetic and real auto loan data demonstrate that our algorithm significantly speeds up learning compared with prior-independent algorithms.