Bayesian dithering for learning: Asymptotically optimal policies in dynamic pricing
成果类型：
Article
署名作者：
Huh, Woonghee Tim; Kim, Michael Jong; Lin, Meichun
署名单位：
University of British Columbia
刊物名称：
PRODUCTION AND OPERATIONS MANAGEMENT
ISSN/ISSBN：
1059-1478
DOI：
10.1111/poms.13786
发表日期：
2022
页码：
3576-3593
关键词：
摘要：
We consider a dynamic pricing and learning problem where a seller prices multiple products and learns from sales data about unknown demand. We study the parametric demand model in a Bayesian setting. To avoid the classical problem of incomplete learning, we propose dithering policies under which prices are probabilistically selected in a neighborhood surrounding the myopic optimal price. By analyzing the effect of dithering in facilitating learning, we establish regret upper bounds for three typical settings of demand model. We show that the dithering policy achieves an upper bound of order logT$\log T$ when the parameter set is finite. It can be modified to achieve a constant regret bound under an additional assumption. We also prove an upper bound of order TlogT$\sqrt {T\log T}$ when the parameter set is compact and convex. Each bound matches (up to a logarithmic factor) the existing lower bound of any pricing policy. In this way, we show that dithering policies achieve asymptotically optimal performance in three different parameter settings, which demonstrates dithering as a unified approach to strike the balance between exploration and exploitation.