On Lai's Upper Confidence Bound in Multi-Armed Bandits

Autor:	Ren, Huachen, Zhang, Cun-Hui
Rok vydání:	2024
Předmět:	Statistics - Machine Learning Computer Science - Machine Learning Mathematics - Statistics Theory 62L05 62L10 (Primary) 68T05 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 25 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2410.02279 Zobrazit plný text záznamu View this record from Arxiv