报告人：胡江 教授
报告题目：Asymptotic properties of a multicolored random reinforced urn model with an application to multi-armed bandits
报告时间：2026年4月13日（周一）15:40-16:20
报告地点：云龙校区6号楼304报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
胡江，教授，博士生导师，入选“国家高层次人才特殊支持计划”青年拔尖人才。主要从事大维随机矩阵理论与大维统计分析研究，研究兴趣包括大维随机矩阵特征根与特征向量的极限性质、高维估计与假设检验、机器学习模型的可解释性。2012年博士毕业于东北师范大学，先后在新加坡国立大学、新加坡南洋理工大学、澳门大学、日本广岛大学、香港科技大学等学府访学。主持多项国家自然科学基金，发表SCI论文四十余篇，其中包括学科权威期刊The Annals of Statistics、Bernoulli、IEEE Transactions on Information Theory等，目前担任SCI杂志Random Matrices: Theory and Applications主编。
报告摘要：
The random self-reinforcement mechanism, characterized by the principle of ``the rich get richer'', has demonstrated significant utility across various domains. One prominent model embodying this mechanism is the random reinforcement urn model. This paper investigates a multicolored, multiple-drawing variant of the random reinforced urn model. We establish the limiting behavior of the normalized urn composition and demonstrate strong convergence upon scaling the counts of each color. Additionally, we derive strong convergence estimators for the reinforcement means, i.e., for the expectations of the replacement matrix's diagonal elements, and prove their joint asymptotic normality. It is noteworthy that the estimators of the largest reinforcement mean are asymptotically independent of the estimators of the other smaller reinforcement means. Additionally, if a reinforcement mean is not the largest, the estimators of these smaller reinforcement means will also demonstrate asymptotic independence among themselves. Furthermore, we explore the parallels between the reinforced mechanisms in random reinforced urn models and multi-armed bandits, addressing hypothesis testing for expected payoffs in the latter context.
