Convergence of Entropy-Regularized Natural Policy Gradient with Linear Function Approximation

SIAM Journal on Optimization, Volume 34, Issue 3, Page 2729-2755, September 2024.
Abstract. 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 [math] 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.