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

Yang, Yuhong ; Zhu, Dan

Ann. Statist., Tome 30 (2002) no. 1, p. 100-121 / Harvested from Project Euclid

Résumé

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.

Détail

Publié le : 2002-02-14
Classification:  Multi-armed bandits,  sequential allocation,  randomized allocation,  con-comitant variable,  nonparametric regression,  62L05,  62C25