报告题目：An Upper Confidence Bound Approach to Estimating the Maximum Mean
报告平台：腾讯会议 (会议ID：709 968 812)
Prof. Guangwu Liu is currently the acting head of Department of Management Sciences, College of Business at City University of Hong Kong. His research interests include stochastic simulation, machine learning, business analytics, financial engineering and risk management. He has published in top journals of the field, including Operations Research, Management Science, INFORMS Journal on Computing, and ACM Transactions on Modeling and Computer Simulation. He has been serving as an associate editor of Naval Research Logistics since 2018.
Estimating the maximum mean of a number of stochastic systems ﬁnds a variety of applications in both management science and machine learning, ranging from ﬁnancial risk measurement and Markov decision processes to reinforcement learning and Monte Carlo tree search. In this work, we study the estimation of the maximum mean under a generalized upper conﬁdence bound (UCB) framework where the sampling budget is sequentially allocated to one of the systems. We study in depth the existing Grand Average (GA) estimator and propose a new Largest-Size Average (LSA) estimator. Speciﬁcally, we establish statistical guarantees, including strong consistency, central limit theorems (CLTs), and asymptotic mean squared errors for both estimators, which are new to the literature. We further construct asymptotically valid conﬁdence intervals based on CLTs. Statistical eﬃciency of the resulting point and interval estimators is demonstrated via numerical examples.
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