Abstract
Banditstyle algorithms have been studied extensively in stochastic and adversarial settings. Such algorithms have been shown to be useful in multiplayer settings, e.g. to solve the wireless network selection problem, which can be formulated as an adversarial bandit problem. A leading bandit algorithm for the adversarial setting is EXP3. However, network behavior is often repetitive, where user density and network behavior follow regular patterns. Bandit algorithms, like EXP3, fail to provide good guarantees for periodic behaviors. A major reason is that these algorithms compete against fixedaction policies, which is ineffective in a periodic setting.
In this paper, we define a periodic bandit setting, and periodic regret as a better performance measure for this type of setting. Instead of comparing an algorithm's performance to fixedaction policies, we aim to be competitive with policies that play arms under some set of possible periodic patterns F (for example, all possible periodic functions with periods 1,2,*s,P). We propose Periodic EXP4, a computationally efficient variant of the EXP4 algorithm for periodic settings. With K arms, T time steps, and where each periodic pattern in F is of length at most P, we show that the periodic regret obtained by Periodic EXP4 is at most O(sqrt{PKT log K + KT log F}). We also prove a lower bound of Omega (sqrt{PKT + KT {log F}/{log K}}) for the periodic setting, showing that this is optimal within logfactors. As an example, we focus on the wireless network selection problem. Through simulation, we show that Periodic EXP4 learns the periodic pattern over time, adapts to changes in a dynamic environment, and far outperforms EXP3.
BibTeX  Entry
@InProceedings{oh_et_al:LIPIcs:2019:10725,
author = {Shunhao Oh and Anuja Meetoo Appavoo and Seth Gilbert},
title = {{Periodic Bandits and Wireless Network Selection}},
booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
pages = {149:1149:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959771092},
ISSN = {18688969},
year = {2019},
volume = {132},
editor = {Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10725},
URN = {urn:nbn:de:0030drops107251},
doi = {10.4230/LIPIcs.ICALP.2019.149},
annote = {Keywords: multiarmed bandits, wireless network selection, periodicity in environment}
}
Keywords: 

multiarmed bandits, wireless network selection, periodicity in environment 
Collection: 

46th International Colloquium on Automata, Languages, and Programming (ICALP 2019) 
Issue Date: 

2019 
Date of publication: 

04.07.2019 
Supplementary Material: 

Source code: https://github.com/Ohohcakester/PeriodicEXP4Source 