Policy gradient in Lipschitz Markov Decision Processes

This paper is about the exploitation of Lipschitz continuity properties for Markov Decision Processes to safely speed up policy-gradient algorithms. Starting from assumptions about the Lipschitz continuity of the state-transition model, the reward function, and the policies considered in the learning process, we show that both the expected return of a policy and its gradient are Lipschitz continuous w.r.t. policy parameters. By leveraging such properties, we define policy-parameter updates that guarantee a performance improvement at each iteration. The proposed methods are empirically evaluated and compared to other related approaches using different configurations of three popular control scenarios: the linear quadratic regulator, the mass-spring-damper system and the ship-steering control.