Optimal Best-Arm Identification in Bandits with Access to Offline Data
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Learning paradigms based purely on offline data as well as those based solely on sequential online learning have been well-studied in the literature. In this paper, we consider combining offline data with online learning, an area less studied but of obvious practical importance. We consider the stochastic K-armed bandit problem, where our goal is to identify the arm with the highest mean in the presence of relevant offline data, with confidence 1-δ. We conduct a lower bound analysis on policies that provide such 1-δ probabilistic correctness guarantees. We develop algorithms that match the lower bound on sample complexity when δ is small. Our algorithms are computationally efficient with an average per-sample acquisition cost of Õ(K), and rely on a careful characterization of the optimality conditions of the lower bound problem.
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