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

Abstract

-cross 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.

Authors 3

Johannes M\"uller, Semih \c{C}ayc{\i}, Guido Mont\'ufar

Specification

Official page: arxiv.org/abs/2403.19448
Source:arXiv (Atom API + RSS)T1observed 7 h agohigh
Arxiv announce type: replace
Source:arXiv (Atom API + RSS)T1observed 7 h agohigh
arXiv id: 2403.19448
Source:arXiv (Atom API + RSS)T1observed 7 h agohigh
Categories: math.OC, cs.LG, cs.NA, cs.SY, eess.SY, math.NA, stat.ML
Source:arXiv (Atom API + RSS)T1observed 7 h agohigh
DOI: 10.1137/24M1653422
Source:arXiv (Atom API + RSS)T1observed 7 h agohigh
PDF: arxiv.org/pdf/2403.19448
Source:arXiv (Atom API + RSS)T1observed 7 h agohigh
Primary category: math.OC
Source:arXiv (Atom API + RSS)T1observed 7 h agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 7 h agohigh

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10

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T110

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7 h ago

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Authors: Johannes M\"uller, Semih \c{C}ayc{\i}, Guido Mont\'ufar

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10 claims · 10 properties

Official pageofficial_url1

Claim history for Official page
Value	Valid from → to	Status	Source	Confidence	Extractor
https://arxiv.org/abs/2403.19448	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Abstractabstract1

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-cross 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.	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Arxiv announce typearxiv_announce_type1

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replace	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

arXiv idarxiv_id1

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2403.19448	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Authorsauthors1

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Value	Valid from → to	Status	Source	Confidence	Extractor
Johannes M\"uller, Semih \c{C}ayc{\i}, Guido Mont\'ufar	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Categoriescategories1

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math.OC, cs.LG, cs.NA, cs.SY, eess.SY, math.NA, stat.ML	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

DOIdoi1

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10.1137/24M1653422	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

PDFpdf_url1

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https://arxiv.org/pdf/2403.19448	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Primary categoryprimary_category1

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math.OC	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Publishedpublished_at1

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11 Sept 2026	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

11 Sept 2026
New paperPaperFisher-Rao Gradient Flows of Linear Programs and State-Action Natural Policy Gradients
New paper: Fisher-Rao Gradient Flows of Linear Programs and State-Action Natural Policy Gradients
arxiv
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Source documents
Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	5 h ago	1

Tier 1 = official/primary, 2 = quality secondary, 3 = community, 4 = unverified. Every snapshot is archived; see all sources and the methodology.