The Annals of Statistics
- Ann. Statist.
- Volume 30, Number 1 (2002), 100-121.
Randomized Allocation with nonparametric estimation for a multi-armed bandit problem with covariates
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.
Ann. Statist., Volume 30, Number 1 (2002), 100-121.
First available in Project Euclid: 5 March 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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