【Academic Seminar】An Upper Confidence Bound Approach to Estimating the Maximum Mean - Prof. Guangwu Liu
Topic: An Upper Confidence Bound Approach to Estimating the Maximum Mean
Speaker: Prof. Guangwu Liu, City University of Hong Kong
Date and Time: 15:30 - 16:30, Friday, November 22, 2019
Venue: Boardroom, Dao Yuan Building
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.
Dr. Guangwu Liu is currently a professor in the Department of Management Sciences, College of Business at City University of Hong Kong. His research interests include stochastic simulation and machine learning, with applications in financial engineering and risk management. He has published in various journals, including ACM Transactions on Modeling and Computer Simulation, INFORMS Journal on Computing, Management Science, and Operations Research. He currently serves as an associate editor for Naval Research Logistics.