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arXiv · 1908.01228

Nonparametric Contextual Bandits in an Unknown Metric Space

Nirandika Wanigasekara·Christina Lee Yu
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Abstract

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.

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Nirandika Wanigasekara, Christina Lee Yu. 2019-08-03. Nonparametric Contextual Bandits in an Unknown Metric Space. https://arxiv.org/abs/1908.01228

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