题　目：Match Made with Matrix Completion: Efficient Offline and Online Learning in Matching Markets

嘉　宾：徐侃，助理教授，亚利桑那州立大学

主持人：江浦平 助理教授 BAT365唯一官网

时　间：2024年9月25日（周三）10:00-11:30am

地　点：安泰楼B207室

内容简介：

Online matching markets face increasing needs to accurately learn the matching qualities between demand and supply for effective design of matching policies. However, the growing diversity of participants introduces a high-dimensional challenge in practice, as there are a substantial number of unknown matching rewards, and learning all rewards requires a large amount of data. We leverage a natural low-rank matrix structure of the matching rewards in these two-sided markets, and propose to utilize matrix completion (i.e., the nuclear norm regularization method) to accelerate the reward learning process with only a small amount of offline data. A key challenge in our setting is that the matrix entries are observed with matching interference, distinct from the independent sampling assumed in existing matrix completion literature. We propose a new proof technique and prove a near-optimal average accuracy guarantee with improved dependence on the matrix dimensions. Furthermore, to guide matching decisions, we develop a novel ''double-enhancement'' procedure that can refine the nuclear norm regularized estimates and further provide a near-optimal entry-wise estimation. Our paper makes the first investigation into adopting matrix completion technique for matching problems. We also extend our approach to online learning settings for both optimal matching and stable matching by incorporating matrix completion in multi-armed bandit algorithms. We present improved regret bounds in matrix dimensions through reduced costs during the exploration phase. Finally, we demonstrate the practical value of our methods using both synthetic data and real data of labor markets.

演讲人简介：

Kan Xu is currently an Assistant Professor of Information Systems at Arizona State University, W. P. Carey School of Business. Previously, he obtained his PhD degree from University of Pennsylvania, Department of Economics under the supervision of Hamsa Bastani. He received a B.S. in Mathematics and a B.A. in Economics from Tsinghua University, and a M.S. in Statistics from University of Chicago. His research focuses on developing novel machine learning methods for data-driven decision making practices, with applications to healthcare, textual analytics, digital platform, and pricing.

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