Global Convergence of Natural Policy Gradient with Hessian-aided Momentum Variance Reduction

Natural policy gradient (NPG) and its variants are widely-used policy search methods in reinforcement learning. Inspired by prior work, a new NPG variant coined NPG-HM is developed in this paper, which utilizes the Hessian-aided momentum technique for variance reduction, while the sub-problem is solved via the stochastic gradient descent method. It is shown that NPG-HM can achieve the global last iterate $\epsilon$-optimality with a sample complexity of $\mathcal{O}(\epsilon^{-2})$, which is the best known result for natural policy gradient type methods under the generic Fisher non-degenerate policy parameterizations. The convergence analysis is built upon a relaxed weak gradient dominance property tailored for NPG under the compatible function approximation framework, as well as a neat way to decompose the error when handling the sub-problem. Moreover, numerical experiments on Mujoco-based environments demonstrate the superior performance of NPG-HM over other state-of-the-art policy gradient methods.

On the Linear Convergence of Policy Gradient under Hadamard Parameterization

The convergence of deterministic policy gradient under the Hadamard parametrization is studied in the tabular setting and the global linear convergence of the algorithm is established. To this end, we first show that the error decreases at an $O(\frac{1}{k})$ rate for all the iterations. Based on this result, we further show that the algorithm has a faster local linear convergence rate after $k_0$ iterations, where $k_0$ is a constant that only depends on the MDP problem and the step size. Overall, the algorithm displays a linear convergence rate for all the iterations with a loose constant than that for the local linear convergence rate.