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

Convergence and Optimality of Policy Gradient Methods in Weakly Smooth Settings