Compactly Restrictable Metric Policy Optimization Problems
This work provides a theoretical framework for continuous control systems, particularly in robotics, but is incremental as it builds on existing dynamic programming methods.
The paper tackles the theoretical well-posedness of policy optimization problems for deterministic Markov decision processes with metric spaces, introducing Compactly Restrictable MPOPs to capture robotic systems and showing they admit solutions via dynamic programming, with applications to feedback linearizable control affine systems.
We study policy optimization problems for deterministic Markov decision processes (MDPs) with metric state and action spaces, which we refer to as Metric Policy Optimization Problems (MPOPs). Our goal is to establish theoretical results on the well-posedness of MPOPs that can characterize practically relevant continuous control systems. To do so, we define a special class of MPOPs called Compactly Restrictable MPOPs (CR-MPOPs), which are flexible enough to capture the complex behavior of robotic systems but specific enough to admit solutions using dynamic programming methods such as value iteration. We show how to arrive at CR-MPOPs using forward-invariance. We further show that our theoretical results on CR-MPOPs can be used to characterize feedback linearizable control affine systems.