Periodica Mathematica Hungarica
Volume/Issue:
Volume 61: Issue 1-2
UCB revisited: Improved regret bounds for the stochastic multi-armed bandit problem
Authors:
Peter Auer Lehrstuhl für Informationstechnologie, Montanuniversität Leoben, Franz-Josef-Straße 18, A-8700 Leoben, Austria

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and
Ronald Ortner Lehrstuhl für Informationstechnologie, Montanuniversität Leoben, Franz-Josef-Straße 18, A-8700 Leoben, Austria

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Pages:
55–65
Online Publication Date:
01 Oct 2010
Publication Date:
01 Sep 2010
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10998-010-3055-6
Keywords:
68T05; 62M05; 91A60; multi-armed bandit problem; regret
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Abstract  

In the stochastic multi-armed bandit problem we consider a modification of the UCB algorithm of Auer et al. [4]. For this modified algorithm we give an improved bound on the regret with respect to the optimal reward. While for the original UCB algorithm the regret in K-armed bandits after T trials is bounded by const ·
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\frac{{K\log (T)}} {\Delta }$$ \end{document}
, where Δ measures the distance between a suboptimal arm and the optimal arm, for the modified UCB algorithm we show an upper bound on the regret of const ·
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\frac{{K\log (T\Delta ^2 )}} {\Delta }$$ \end{document}
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Cover Periodica Mathematica Hungarica
Periodica Mathematica Hungarica
Print ISSN:
0031-5303
Online ISSN:
1588-2829

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Periodica Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1971
Volumes
per Year		 2
Issues
per Year		 4
Founder Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's
Address		 H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0031-5303 (Print)
ISSN 1588-2829 (Online)

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