Convergence of Policy Mirror Descent Beyond Compatible Function Approximation

• URL: http://arxiv.org/abs/2502.11033v1
• Date: Sun, 16 Feb 2025 08:05:46 GMT
• Title: Convergence of Policy Mirror Descent Beyond Compatible Function Approximation
• Authors: Uri Sherman, Tomer Koren, Yishay Mansour,
• Abstract summary: We develop theoretical PMD general policy classes where we strictly assume a weaker variational dominance and obtain convergence to the best-in-class policy. Our main notion leverages a novel notion induced by the local norm induced by the occupancy- gradient measure.
• Score: 66.4260157478436
• License:
• Abstract: 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.

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