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arXiv · 2309.03145

The Best Arm Evades: Near-optimal Multi-pass Streaming Lower Bounds for Pure Exploration in Multi-armed Bandits

Sepehr Assadi·Chen Wang
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Abstract

We give a near-optimal sample-pass trade-off for pure exploration in multi-armed bandits (MABs) via multi-pass streaming algorithms: any streaming algorithm with sublinear memory that uses the optimal sample complexity of $O(\frac{n}{Δ^2})$ requires $Ω(\frac{\log{(1/Δ)}}{\log\log{(1/Δ)}})$ passes. Here, $n$ is the number of arms and $Δ$ is the reward gap between the best and the second-best arms. Our result matches the $O(\log(\frac{1}Δ))$-pass algorithm of Jin et al. [ICML'21] (up to lower order terms) that only uses $O(1)$ memory and answers an open question posed by Assadi and Wang [STOC'20].

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Sepehr Assadi, Chen Wang. 2024-06-25. The Best Arm Evades: Near-optimal Multi-pass Streaming Lower Bounds for Pure Exploration in Multi-armed Bandits. https://arxiv.org/abs/2309.03145

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