2025/02/16 by Uri Sherman, Sherman, Uri, Tomer Koren +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Applied mathematics #Biology #Computer science #Convergence (economics) #Descent (aeronautics) #Econometrics #Economic Policies and Impacts #Economic growth #Economics #Evolutionary biology #FOS: Computer and information sciences #FOS: Mathematics #Function (biology) #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematical economics #Mathematics #Optimization and Control (math.OC) #Physics
paper · pdf · doi:10.48550/arxiv.2502.11033
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.