Before revision:  Next, our main result establishes an episode complexity of O(H^2/d_m\epsilon^2) for  \emph{local} uniform convergence that applies to all \emph{near-empirically optimal} policies for the MDPs with \emph{stationary} transition.
After revision:  Next, our main result establishes an upper bound of O(H^2/d_m\epsilon^2) for \emph{local} uniform convergence that applies to all \emph{near-empirically optimal} policies for the MDPs with \emph{stationary} transition.