CONVERGENCE OF ENTROPY-REGULARIZED NATURAL POLICY GRADIENT WITH LINEAR FUNCTION APPROXIMATION

Natural policy gradient (NPG) methods, equipped with function approximation and entropy regularization, achieve impressive empirical success in reinforcement learning problems with large state-action spaces. However, their convergence properties and the impact of entropy regularization remain elusive in the function approximation regime. In this paper, we establish finite- time convergence analyses of entropy-regularized NPG with linear function approximation under softmax parameterization. In particular, we prove that entropy-regularized NPG with averaging satisfies the persistence of excitation condition, and achieves a fast convergence rate of (O) over tilde (1/T) up to a function approximation error in regularized Markov decision processes. This convergence result does not require any a priori assumptions on the policies. Furthermore, under mild regularity conditions on the concentrability coefficient and basis vectors, we prove that entropy-regularized NPG exhibits linear convergence up to the compatible function approximation error. Finally, we provide sample complexity results for sample-based NPG with entropy regularization.