  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 the non-stationary
kernel bandit setting. Moreover, when applied to the non-stationary linear
bandit setting by using 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.
