时 间：2023年6月8日（周四）15：00-16：00
地 点: 理科大楼A1514室
题 目：Online Statistical Inference for Matrix Contextual Bandit
报告人：Yichen Zhang 助理教授，Purdue University
主持人：王小舟 助理教授
主 办：统计学院
摘 要：
Contextual bandit has been widely used for sequential decision-making based on the current contextual information and historical feedback data. In modern applications, such context format can be rich and can often be formulated as a matrix. Moreover, while existing bandit algorithms mainly focused on reward-maximization, less attention has been paid to the statistical inference. To fill in these gaps, in this work we consider a matrix contextual bandit framework where the true model parameter is a low-rank matrix, and propose a fully online procedure to simultaneously make sequential decision-making and conduct statistical inference. The low-rank structure of the model parameter and the adaptivity nature of the data collection process makes this difficult: standard low-rank estimators are not fully online and are biased, while existing inference approaches in bandit algorithms fail to account for the low-rankness and are also biased. To address these, we introduce a new online doubly-debiasing inference procedure to simultaneously handle both sources of bias. In theory, we establish the asymptotic normality of the proposed online doubly-debiased estimator and prove the validity of the constructed confidence interval. Our inference results are built upon a newly developed low-rank stochastic gradient descent estimator and its non-asymptotic convergence result, which is also of independent interest.
This work is joint with Qiyu Han and Will Wei Sun at Purdue University.
报告人简介：
Yichen Zhang is an assistant professor of Quantitative Methods at Daniels School of Business, Purdue University. Prior to joining Purdue, Yichen earned his Ph.D. from the Department of Technology, Operations, and Statistics at Stern School of Business at New York University in 2020. Before that, he received his Bachelors in Mathematics and Economics from Peking University in 2015. Yichen has worked at the intersection of statistics, optimization, and machine learning. His research focuses on statistical inference for online streaming data, distributed estimation and inference, time series analysis, nonsmooth optimization, supply chains and other business problems with statistical models.