Please use this identifier to cite or link to this item:
https://scholarbank.nus.edu.sg/handle/10635/184300
Title: | THE CONFIDENCE BOUND METHOD FOR THE MULTI-ARMED BANDIT PROBLEM WITH LARGE ARM SIZE | Authors: | HU SHOURI | Keywords: | confidence bound method, large arm size, multi-armed bandit, optimality, regret lower bound. | Issue Date: | 6-Jul-2020 | Citation: | HU SHOURI (2020-07-06). THE CONFIDENCE BOUND METHOD FOR THE MULTI-ARMED BANDIT PROBLEM WITH LARGE ARM SIZE. ScholarBank@NUS Repository. | Abstract: | We consider two modifications of the confidence bound method that achieve optimality in the case of large arm sizes. In the first situation we assume the arm size is infinitely large. We establish a regret lower bound and construct confidence bounds that achieve the regret lower bound asymptotically. A novel feature of these confidence bounds is a target value for deciding whether to stick to arms that have been played, or to play a new arm. In the second situation we consider asymptotics when the arm size grows at a polynomial rate with respect to the number of trials. We show that the regret lower bound has an expression similar to that of Lai and Robbins (1985), but with a smaller asymptotic constant. We show how the confidence bounds proposed by Agarwal (1995) can be corrected for arm size so that the new regret lower bound is achieved. | URI: | https://scholarbank.nus.edu.sg/handle/10635/184300 |
Appears in Collections: | Ph.D Theses (Open) |
Show full item record
Files in This Item:
File | Description | Size | Format | Access Settings | Version | |
---|---|---|---|---|---|---|
HuS.pdf | 941.03 kB | Adobe PDF | OPEN | None | View/Download |
Google ScholarTM
Check
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.