Nonparametric Contextual Bandits in an Unknown Metric Space
This work addresses efficient learning in multi-arm bandit problems for applications like recommendation systems, though it appears incremental by building on existing nonparametric and metric-based methods.
The paper tackles the problem of nonparametric contextual bandits with many arms and unknown structure among reward functions, presenting a novel algorithm that learns arm similarities and adaptively partitions the context-arm space, achieving regret bounds and demonstrating performance dependent on local geometry in simulations.
Consider a nonparametric contextual multi-arm bandit problem where each arm $a \in [K]$ is associated to a nonparametric reward function $f_a: [0,1] \to \mathbb{R}$ mapping from contexts to the expected reward. Suppose that there is a large set of arms, yet there is a simple but unknown structure amongst the arm reward functions, e.g. finite types or smooth with respect to an unknown metric space. We present a novel algorithm which learns data-driven similarities amongst the arms, in order to implement adaptive partitioning of the context-arm space for more efficient learning. We provide regret bounds along with simulations that highlight the algorithm's dependence on the local geometry of the reward functions.