  This paper develops the first policy gradient method with global optimality
guarantee and complexity analysis for robust reinforcement learning under model
mismatch. Robust reinforcement learning is to learn a policy robust to model
mismatch between simulator and real environment. We first develop the robust
policy (sub-)gradient, which is applicable for any differentiable parametric
policy class. We show that the proposed robust policy gradient method converges
to the global optimum asymptotically under direct policy parameterization. We
further develop a smoothed robust policy gradient method and show that to
achieve an $\epsilon$-global optimum, the complexity is $\mathcal
O(\epsilon^{-3})$. We then extend our methodology to the general model-free
setting and design the robust actor-critic method with differentiable
parametric policy class and value function. We further characterize its
asymptotic convergence and sample complexity under the tabular setting.
Finally, we provide simulation results to demonstrate the robustness of our
methods.
