今日云讲堂 | 夏冬：通过矩阵补全进行在线策略学习与推断

统计之都 · 公众号 · · 2024-05-09 22:43

正文

报告信息

主题：Online Policy Learning and Inference by Matrix Completion

嘉宾：夏冬

地点：腾讯会议：920-361-274（或点击阅读原文）

时间：2024年05月10日（周五）20:00

报告摘要

Making online decisions can be challenging when features are sparse and orthogonal to historical ones, especially when the optimal policy is learned through collaborative filtering. We formulate the problem as a matrix completion bandit (MCB), where the expected reward under each arm is characterized by an unknown low-rank matrix. The ε-greedy bandit and the online gradient descent algorithm are explored. Policy learning and regret performance are studied under a specific schedule for exploration probabilities and step sizes. A faster decaying exploration probability yields smaller regret but learns the optimal policy less accurately. We investigate an online debiasing method based on inverse propensity weighting (IPW) and a general framework for online policy inference. The IPW-based estimators are asymptotically normal under mild arm-optimality conditions. Numerical simulations corroborate our theoretical findings. Our methods are applied to the San Francisco parking pricing project data, revealing intriguing discoveries and outperforming the benchmark policy.

嘉宾简介

Dr. Dong XIA is an Assistant Professor in Department of Mathematics at Hong Kong University of Science and Technology. He was a Postdoctral Research Scientist in Department of Statistics at Columbia University and a Visiting Assistant Professor in Department of Statistics at University of Wisconsin-Madison. He obtained his Ph.D. in Computational Science and Enginering and Mathematics from Georgia Institute of Technology in 2016. His research interest lies in high-dimensional statistics, machine learning theory and optimization. He is currently an Associate Editor of Journal of Statistical Planning and Inference.