  In this paper, we propose a novel perturbation-based exploration method in
bandit algorithms with bounded or unbounded rewards, called residual bootstrap
exploration (\texttt{ReBoot}). The \texttt{ReBoot} enforces exploration by
injecting data-driven randomness through a residual-based perturbation
mechanism. This novel mechanism captures the underlying distributional
properties of fitting errors, and more importantly boosts exploration to escape
from suboptimal solutions (for small sample sizes) by inflating variance level
in an \textit{unconventional} way. In theory, with appropriate variance
inflation level, \texttt{ReBoot} provably secures instance-dependent
logarithmic regret in Gaussian multi-armed bandits. We evaluate the
\texttt{ReBoot} in different synthetic multi-armed bandits problems and observe
that the \texttt{ReBoot} performs better for unbounded rewards and more
robustly than \texttt{Giro} \cite{kveton2018garbage} and \texttt{PHE}
\cite{kveton2019perturbed}, with comparable computational efficiency to the
Thompson sampling method.
