An Optimization-based Algorithm for Non-stationary Kernel Bandits without Prior Knowledge
Kihyuk Hong, Yuhang Li, Ambuj Tewari
Abstract
We propose an algorithm for non-stationary kernel bandits that does not require prior knowledge of the degree of non-stationarity. The algorithm follows randomized strategies obtained by solving optimization problems that balance exploration and exploitation. It adapts to non-stationarity by restarting when a change in the reward function is detected. Our algorithm enjoys a tighter dynamic regret bound than previous work on non- stationary kernel bandits. Moreover, when applied to the non-stationary linear bandits by us- ing a linear kernel, our algorithm is nearly minimax optimal, solving an open problem in the non-stationary linear bandit literature. We extend our algorithm to use a neural network for dynamically adapting the feature mapping to observed data. We prove a dynamic regret bound of the extension using the neural tangent kernel theory. We demonstrate empirically that our algorithm and the extension can adapt to varying degrees of non-stationarity.
BibTeX
@InProceedings{pmlr-v206-hong23b,
title = {An Optimization-based Algorithm for Non-stationary Kernel Bandits without Prior Knowledge},
author = {Hong, Kihyuk and Li, Yuhang and Tewari, Ambuj},
booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics},
pages = {3048--3085},
year = {2023},
editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem},
volume = {206},
series = {Proceedings of Machine Learning Research},
month = {25--27 Apr},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v206/hong23b/hong23b.pdf},
url = {https://proceedings.mlr.press/v206/hong23b.html},
abstract = {We propose an algorithm for non-stationary kernel bandits that does not require prior knowledge of the degree of non-stationarity. The algorithm follows randomized strategies obtained by solving optimization problems that balance exploration and exploitation. It adapts to non-stationarity by restarting when a change in the reward function is detected. Our algorithm enjoys a tighter dynamic regret bound than previous work on non- stationary kernel bandits. Moreover, when applied to the non-stationary linear bandits by us- ing a linear kernel, our algorithm is nearly minimax optimal, solving an open problem in the non-stationary linear bandit literature. We extend our algorithm to use a neural network for dynamically adapting the feature mapping to observed data. We prove a dynamic regret bound of the extension using the neural tangent kernel theory. We demonstrate empirically that our algorithm and the extension can adapt to varying degrees of non-stationarity.}
}