Convergence of Policy Mirror Descent Beyond Compatible Function Approximation
This work addresses a foundational problem in reinforcement learning theory for researchers and practitioners, providing incremental theoretical improvements for policy optimization methods.
The paper tackles the theoretical convergence limitations of policy mirror descent (PMD) in large-scale environments with parametric policies, by developing a framework that replaces strong closure conditions with a weaker variational gradient dominance assumption and obtains convergence rate bounds to the best-in-class policy.
Modern policy optimization methods roughly follow the policy mirror descent (PMD) algorithmic template, for which there are by now numerous theoretical convergence results. However, most of these either target tabular environments, or can be applied effectively only when the class of policies being optimized over satisfies strong closure conditions, which is typically not the case when working with parametric policy classes in large-scale environments. In this work, we develop a theoretical framework for PMD for general policy classes where we replace the closure conditions with a strictly weaker variational gradient dominance assumption, and obtain upper bounds on the rate of convergence to the best-in-class policy. Our main result leverages a novel notion of smoothness with respect to a local norm induced by the occupancy measure of the current policy, and casts PMD as a particular instance of smooth non-convex optimization in non-Euclidean space.