The Annals of Statistics

Randomized Allocation with nonparametric estimation for a multi-armed bandit problem with covariates

Yuhong Yang and Dan Zhu

Full-text: Open access

Abstract

We study a multi-armed bandit problem in a setting where covariates are 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.

Article information

Source
Ann. Statist., Volume 30, Number 1 (2002), 100-121.

Dates
First available in Project Euclid: 5 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1015362186

Digital Object Identifier
doi:10.1214/aos/1015362186

Mathematical Reviews number (MathSciNet)
MR1892657

Zentralblatt MATH identifier
1012.62088

Subjects
Primary: 62L05: Sequential design 62C25: Compound decision problems

Keywords
Multi-armed bandits sequential allocation randomized allocation con-comitant variable nonparametric regression

Citation

Yang, Yuhong; Zhu, Dan. Randomized Allocation with nonparametric estimation for a multi-armed bandit problem with covariates. Ann. Statist. 30 (2002), no. 1, 100--121. doi:10.1214/aos/1015362186. https://projecteuclid.org/euclid.aos/1015362186


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