  Policy optimization methods are one of the most widely used classes of
Reinforcement Learning (RL) algorithms. Yet, so far, such methods have been
mostly analyzed from an optimization perspective, without addressing the
problem of exploration, or by making strong assumptions on the interaction with
the environment. In this paper we consider model-based RL in the tabular
finite-horizon MDP setting with unknown transitions and bandit feedback. For
this setting, we propose an optimistic trust region policy optimization (TRPO)
algorithm for which we establish $\tilde O(\sqrt{S^2 A H^4 K})$ regret for
stochastic rewards. Furthermore, we prove $\tilde O( \sqrt{ S^2 A H^4 } K^{2/3}
) $ regret for adversarial rewards. Interestingly, this result matches previous
bounds derived for the bandit feedback case, yet with known transitions. To the
best of our knowledge, the two results are the first sub-linear regret bounds
obtained for policy optimization algorithms with unknown transitions and bandit
feedback.
