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: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916299499634688 |
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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 |