Fisher-Rao Gradient Flows of Linear Programs and State-Action Natural Policy Gradients

Abstract:Kakade's natural policy gradient method has been studied extensively in recent years, showing linear convergence with and without regularization. We study another natural gradient method based on the Fisher information matrix of the state-action distributions which has received little attention from the theoretical side. Here, the state-action distributions follow the Fisher-Rao gradient flow inside the state-action polytope with respect to a linear potential. Therefore, we study Fisher-Rao gradient flows of linear programs more generally and show linear convergence with a rate that depends on the geometry of the linear program. Equivalently, this yields an estimate on the error induced by entropic regularization of the linear program which improves existing results. We extend these results and show sublinear convergence for perturbed Fisher-Rao gradient flows and natural gradient flows up to an approximation error. In particular, these general results cover the case of state-action natural policy gradients.

Optimization and Control (math.OC); Machine Learning (cs.LG); Systems and Control (eess.SY); Numerical Analysis (math.NA); Machine Learning (stat.ML)

arXiv:2403.19448 [math.OC]

(or arXiv:2403.19448v3 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2403.19448 Focus to learn more arXiv-issued DOI via DataCite

SIAM Journal on Optimization, Vol. 35, Iss. 2 (2025), 10.1137/24M1653422

https://doi.org/10.1137/24M1653422 Focus to learn more DOI(s) linking to related resources

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