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

Fuente: arXiv
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Autori principali: Assadi, Sepehr, Wang, Chen
Natura: Preprint
Pubblicazione: 2023
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author Assadi, Sepehr
Wang, Chen
author_facet Assadi, Sepehr
Wang, Chen
contents 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].
format Preprint
id arxiv_https___arxiv_org_abs_2309_03145
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle The Best Arm Evades: Near-optimal Multi-pass Streaming Lower Bounds for Pure Exploration in Multi-armed Bandits
Assadi, Sepehr
Wang, Chen
Machine Learning
Data Structures and Algorithms
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].
title The Best Arm Evades: Near-optimal Multi-pass Streaming Lower Bounds for Pure Exploration in Multi-armed Bandits
topic Machine Learning
Data Structures and Algorithms
url https://arxiv.org/abs/2309.03145