Optimal Best-Arm Identification in Bandits with Access to Offline Data

• URL: http://arxiv.org/abs/2306.09048v1
• Date: Thu, 15 Jun 2023 11:12:35 GMT
• Title: Optimal Best-Arm Identification in Bandits with Access to Offline Data
• Authors: Shubhada Agrawal, Sandeep Juneja, Karthikeyan Shanmugam, Arun Sai Suggala
• Abstract summary: We consider combining offline data with online learning, an area less studied but obvious practical importance. We develop algorithms that match the lower bound on sample complexity when $delta$ is small. Our algorithms are computationally efficient with an average per-sample acquisition cost of $tildeO(K)$, and rely on a careful characterization of the optimality conditions of the lower bound problem.
• Score: 27.365122983434887
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $1-\delta$. We conduct a lower bound analysis on policies that provide such $1-\delta$ probabilistic correctness guarantees. We develop algorithms that match the lower bound on sample complexity when $\delta$ is small. Our algorithms are computationally efficient with an average per-sample acquisition cost of $\tilde{O}(K)$, and rely on a careful characterization of the optimality conditions of the lower bound problem.

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