  Some reinforcement learning methods suffer from high sample complexity
causing them to not be practical in real-world situations. $Q$-function reuse,
a transfer learning method, is one way to reduce the sample complexity of
learning, potentially improving usefulness of existing algorithms. Prior work
has shown the empirical effectiveness of $Q$-function reuse for various
environments when applied to model-free algorithms. To the best of our
knowledge, there has been no theoretical work showing the regret of
$Q$-function reuse when applied to the tabular, model-free setting. We aim to
bridge the gap between theoretical and empirical work in $Q$-function reuse by
providing some theoretical insights on the effectiveness of $Q$-function reuse
when applied to the $Q$-learning with UCB-Hoeffding algorithm. Our main
contribution is showing that in a specific case if $Q$-function reuse is
applied to the $Q$-learning with UCB-Hoeffding algorithm it has a regret that
is independent of the state or action space. We also provide empirical results
supporting our theoretical findings.
