  To address the contextual bandit problem, we propose an online random forest
algorithm. The analysis of the proposed algorithm is based on the sample
complexity needed to find the optimal decision stump. Then, the decision stumps
are assembled in a random collection of decision trees, Bandit Forest. We show
that the proposed algorithm is optimal up to logarithmic factors. The
dependence of the sample complexity upon the number of contextual variables is
logarithmic. The computational cost of the proposed algorithm with respect to
the time horizon is linear. These analytical results allow the proposed
algorithm to be efficient in real applications, where the number of events to
process is huge, and where we expect that some contextual variables, chosen
from a large set, have potentially non- linear dependencies with the rewards.
In the experiments done to illustrate the theoretical analysis, Bandit Forest
obtain promising results in comparison with state-of-the-art algorithms.
