On Lai's Upper Confidence Bound in Multi-Armed Bandits
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914964060504064 |
|---|---|
| author | Ren, Huachen Zhang, Cun-Hui |
| author_facet | Ren, Huachen Zhang, Cun-Hui |
| contents | In this memorial paper, we honor Tze Leung Lai's seminal contributions to the topic of multi-armed bandits, with a specific focus on his pioneering work on the upper confidence bound. We establish sharp non-asymptotic regret bounds for an upper confidence bound index with a constant level of exploration for Gaussian rewards. Furthermore, we establish a non-asymptotic regret bound for the upper confidence bound index of Lai (1987) which employs an exploration function that decreases with the sample size of the corresponding arm. The regret bounds have leading constants that match the Lai-Robbins lower bound. Our results highlight an aspect of Lai's seminal works that deserves more attention in the machine learning literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02279 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Lai's Upper Confidence Bound in Multi-Armed Bandits Ren, Huachen Zhang, Cun-Hui Machine Learning Statistics Theory 62L05, 62L10 (Primary) 68T05 (Secondary) In this memorial paper, we honor Tze Leung Lai's seminal contributions to the topic of multi-armed bandits, with a specific focus on his pioneering work on the upper confidence bound. We establish sharp non-asymptotic regret bounds for an upper confidence bound index with a constant level of exploration for Gaussian rewards. Furthermore, we establish a non-asymptotic regret bound for the upper confidence bound index of Lai (1987) which employs an exploration function that decreases with the sample size of the corresponding arm. The regret bounds have leading constants that match the Lai-Robbins lower bound. Our results highlight an aspect of Lai's seminal works that deserves more attention in the machine learning literature. |
| title | On Lai's Upper Confidence Bound in Multi-Armed Bandits |
| topic | Machine Learning Statistics Theory 62L05, 62L10 (Primary) 68T05 (Secondary) |
| url | https://arxiv.org/abs/2410.02279 |