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【学术会议】An Upper Confidence Bound Approach to Estimating the Maximum Mean - Prof. Guangwu Liu

  • 2019.11.22
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An Upper Confidence Bound Approach to Estimating the Maximum Mean

主题: An Upper Confidence Bound Approach to Estimating the Maximum Mean

报告人: Prof. Guangwu Liu, City University of Hong Kong

时间: 15:30 - 16:30, Friday, November 22, 2019

地点: Boardroom, Dao Yuan Building

 

摘要:

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.

 

简介:

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.