  In this paper, we propose new problem-independent lower bounds on the sample
complexity and regret in episodic MDPs, with a particular focus on the
non-stationary case in which the transition kernel is allowed to change in each
stage of the episode. Our main contribution is a novel lower bound of
$\Omega((H^3SA/\epsilon^2)\log(1/\delta))$ on the sample complexity of an
$(\varepsilon,\delta)$-PAC algorithm for best policy identification in a
non-stationary MDP. This lower bound relies on a construction of "hard MDPs"
which is different from the ones previously used in the literature. Using this
same class of MDPs, we also provide a rigorous proof of the
$\Omega(\sqrt{H^3SAT})$ regret bound for non-stationary MDPs. Finally, we
discuss connections to PAC-MDP lower bounds.
