Markov Decision Processes are classically solved using Value Iteration and Policy Iteration algorithms. Recent interest in Reinforcement Learning has motivated the study of methods inspired by optimization, such as gradient ascent. Among these, a popular algorithm is the Natural Policy Gradient, which is a mirror descent variant for MDPs. This algorithm forms the basis of several popular Reinforcement Learning algorithms such as Natural actor-critic, TRPO, PPO, etc, and so is being studied with growing interest. It has been shown that Natural Policy Gradient with constant step size converges with a sublinear rate of O(1/k) to the global optimal. In this paper, we present improved finite time convergence bounds, and show that this algorithm has geometric (also known as linear) asymptotic convergence rate. We further improve this convergence result by introducing a variant of Natural Policy Gradient with adaptive step sizes. Finally, we compare different variants of policy gradient methods experimentally.

本文研究了应用于马尔可夫决策过程中的自然策略梯度算法，在此基础上提出具有自适应步长的改进方法，并通过实验比较不同变种的策略梯度方法。

自然策略梯度算法的线性收敛性