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arXiv · 2505.15643

Optimal Best-Arm Identification under Fixed Confidence with Multiple Optima

Lan V. Truong
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Abstract

We study best-arm identification in stochastic multi-armed bandits under the fixed-confidence setting, focusing on instances with multiple optimal arms. Unlike prior work that addresses the unknown-number-of-optimal-arms case, we consider the setting where the number of optimal arms is known in advance. We derive a new information-theoretic lower bound on the expected sample complexity that leverages this structural knowledge and is strictly tighter than previous bounds. Building on the Track-and-Stop algorithm, we propose a modified, tie-aware stopping rule and prove that it achieves asymptotic instance-optimality, matching the new lower bound. Our results provide the first formal guarantee of optimality for Track-and-Stop in multi-optimal settings with known cardinality, offering both theoretical insights and practical guidance for efficiently identifying any optimal arm.

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Lan V. Truong. 2025-05-21. Optimal Best-Arm Identification under Fixed Confidence with Multiple Optima. https://arxiv.org/abs/2505.15643

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