Abstract #300641


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JSM 2002 Abstract #300641
Activity Number: 149
Type: Contributed
Date/Time: Monday, August 12, 2002 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #300641
Title: Randomized Allocation with Nonparametric Estimation for a Multi-Armed Bandit Problem with Covariates
Author(s): Yuhong Yang*+
Affiliation(s): Iowa State University
Address: 312 Snedecor Hall, Ames, Iowa, 50011, USA
Keywords: multi-armed bandits ; randomized allocation ; concomittant variable ; nonparametric estimation
Abstract:

We study a multi-armed bandit problem in a setting with covariates available. We take a nonparametric approach to estimate the functional relationship between the response (reward) and the covariates. The estimated relationships and appropriate randomization are used to select a good arm to play for a greater expected reward. Randomization helps balance the tendency to trust the currently most promising arm with further exploration of other arms. It is shown that with some familiar nonparametric methods (e.g., histogram), the proposed strategy is strongly consistent in the sense that the accumulated reward is asymptotically equivalent to that based on the best arm (which depends on the covariates) almost surely.


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