  Policy gradient methods have been frequently applied to problems in control
and reinforcement learning with great success, yet existing convergence
analysis still relies on non-intuitive, impractical and often opaque
conditions. In particular, existing rates are achieved in limited settings,
under strict regularity conditions. In this work, we establish explicit
convergence rates of policy gradient methods, extending the convergence regime
to weakly smooth policy classes with $L_2$ integrable gradient. We provide
intuitive examples to illustrate the insight behind these new conditions.
Notably, our analysis also shows that convergence rates are achievable for both
the standard policy gradient and the natural policy gradient algorithms under
these assumptions. Lastly we provide performance guarantees for the converged
policies.
