Nearly Optimal Adaptive Procedure with Change Detection for Piecewise-Stationary Bandit
Yang Cao, Zheng Wen, Branislav Kveton, Yao Xie
Abstract
Multi-armed bandit (MAB) is a class of online learning problems where a learning agent aims to maximize its expected cumulative reward while repeatedly selecting to pull arms with unknown reward distributions. We consider a scenario where the reward distributions may change in a piecewise-stationary fashion at unknown time steps. We show that by incorporating a simple change-detection component with classic UCB algorithms to detect and adapt to changes, our so-called M-UCB algorithm can achieve nearly optimal regret bound on the order of $O(\sqrt{MKT\log T})$, where $T$ is the number of time steps, $K$ is the number of arms, and $M$ is the number of stationary segments. Comparison with the best available lower bound shows that our M-UCB is nearly optimal in $T$ up to a logarithmic factor. We also compare M-UCB with the state-of-the-art algorithms in numerical experiments using a public Yahoo! dataset and a real-world digital marketing dataset to demonstrate its superior performance.
BibTeX
@InProceedings{pmlr-v89-cao19a,
title = {Nearly Optimal Adaptive Procedure with Change Detection for Piecewise-Stationary Bandit},
author = {Cao, Yang and Wen, Zheng and Kveton, Branislav and Xie, Yao},
booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics},
pages = {418--427},
year = {2019},
editor = {Chaudhuri, Kamalika and Sugiyama, Masashi},
volume = {89},
series = {Proceedings of Machine Learning Research},
month = {16--18 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v89/cao19a/cao19a.pdf},
url = {https://proceedings.mlr.press/v89/cao19a.html},
abstract = {Multi-armed bandit (MAB) is a class of online learning problems where a learning agent aims to maximize its expected cumulative reward while repeatedly selecting to pull arms with unknown reward distributions. We consider a scenario where the reward distributions may change in a piecewise-stationary fashion at unknown time steps. We show that by incorporating a simple change-detection component with classic UCB algorithms to detect and adapt to changes, our so-called M-UCB algorithm can achieve nearly optimal regret bound on the order of $O(\sqrt{MKT\log T})$, where $T$ is the number of time steps, $K$ is the number of arms, and $M$ is the number of stationary segments. Comparison with the best available lower bound shows that our M-UCB is nearly optimal in $T$ up to a logarithmic factor. We also compare M-UCB with the state-of-the-art algorithms in numerical experiments using a public Yahoo! dataset and a real-world digital marketing dataset to demonstrate its superior performance.}
}