Optimistic Natural Policy Gradient: a Simple Efficient Policy Optimization Framework for Online RL

While policy optimization algorithms have played an important role in recent empirical success of Reinforcement Learning (RL), the existing theoretical understanding of policy optimization remains rather limited-they are either restricted to tabular MDPs or suffer from highly suboptimal sample complexity, especially in online RL where exploration is necessary. This paper proposes a simple efficient policy optimization framework-OPTIMISTIC NPG for online RL. OPTIMISTIC NPG can be viewed as a simple combination of the classic natural policy gradient (NPG) algorithm [Kakade, 2001] and an optimistic policy evaluation subroutine to encourage exploration. For d-dimensional linear MDPs, OPTIMISTIC NPG is computationally efficient, and learns an ϵ-optimal policy within Õ(d²/ϵ³) samples, which is the first computationally efficient algorithm whose sample complexity has the optimal dimension dependence Θ̃(d²). It also improves over state-of-the-art results of policy optimization algorithms [Zanette et al., 2021] by a factor of d. For general function approximation that subsumes linear MDPs, OPTIMISTIC NPG, to our best knowledge, is also the first policy optimization algorithm that achieves the polynomial sample complexity for learning near-optimal policies.