Periodic Bandits and Wireless Network Selection
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 $1,2,\cdots,P$). 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 $O\big(\sqrt{PKT \log K + KT \log F}\big)$. We also prove a lower bound of $\Omega\big(\sqrt{PKT + KT \frac{\log F}{\log K}} \big)$ 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1904.12355
 Bibcode:
 2019arXiv190412355O
 Keywords:

 Computer Science  Networking and Internet Architecture;
 Computer Science  Machine Learning
 EPrint:
 46th International Colloquium on Automata, Languages and Programming (ICALP 2019), Track C