  We consider the problem of learning to optimize an unknown Markov decision
process (MDP). We show that, if the MDP can be parameterized within some known
function class, we can obtain regret bounds that scale with the dimensionality,
rather than cardinality, of the system. We characterize this dependence
explicitly as $\tilde{O}(\sqrt{d_K d_E T})$ where $T$ is time elapsed, $d_K$ is
the Kolmogorov dimension and $d_E$ is the \emph{eluder dimension}. These
represent the first unified regret bounds for model-based reinforcement
learning and provide state of the art guarantees in several important settings.
Moreover, we present a simple and computationally efficient algorithm
\emph{posterior sampling for reinforcement learning} (PSRL) that satisfies
these bounds.
