Towards Minimax Optimal Best Arm Identification in Linear Bandits

• URL: http://arxiv.org/abs/2105.13017v1
• Date: Thu, 27 May 2021 09:19:10 GMT
• Title: Towards Minimax Optimal Best Arm Identification in Linear Bandits
• Authors: Junwen Yang, Vincent Y. F. Tan
• Abstract summary: We study the problem of best arm identification in linear bandits in the fixed-budget setting. By leveraging properties of the G-optimal design and incorporating it into the arm allocation rule, we design a parameter-free algorithm. We provide a theoretical analysis of the failure probability of OD-LinBAI.
• Score: 95.22854522340938
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the problem of best arm identification in linear bandits in the fixed-budget setting. By leveraging properties of the G-optimal design and incorporating it into the arm allocation rule, we design a parameter-free algorithm, Optimal Design-based Linear Best Arm Identification (OD-LinBAI). We provide a theoretical analysis of the failure probability of OD-LinBAI. While the performances of existing methods (e.g., BayesGap) depend on all the optimality gaps, OD-LinBAI depends on the gaps of the top $d$ arms, where $d$ is the effective dimension of the linear bandit instance. Furthermore, we present a minimax lower bound for this problem. The upper and lower bounds show that OD-LinBAI is minimax optimal up to multiplicative factors in the exponent. Finally, numerical experiments corroborate our theoretical findings.

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