Adaptive Sampling Methods for Ranking and Estimation Problems

This project aims to propose adaptive sampling methods for ranking and estimation problems that concern a number of stochastic systems with unknown means. These problems find applications in operations research, e.g., measurement of financial risk, and in healthcare management, e.g., inference of adaptive experiments in clinical trials. Our primary focus in this project is on the development of adaptive sampling methods for identifying the system with the mth largest mean among K stochastic systems, and estimating its mean. We plan to investigate adaptive sampling methods including epsilon-Greedy and upper confidence bound (UCB) policies, propose a unified framework for studying various estimators for the mean of the ranked system, and provide theoretical supports to the proposed sampling methods and the ranked-mean estimators. We shall further apply the proposed adaptive sampling methods and estimators to several important applications, including the measurement of portfolio risk, and hypothesis testing in clinical trials.