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

arXiv:2403.19448 · math.OC, cs.LG, cs.NA, cs.SY, eess.SY, math.NA, stat.ML · Submitted 2024-03-28 · Read on arXiv

math.OC, cs.LG, cs.NA, cs.SY, eess.SY, math.NA, stat.ML

Submitted: 2024-03-28

Updated: 2026-09-10

Comments: 25 pages, 4 figures, to appear at SIAM Journal on Optimization

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

DOI: 10.1137/24M1653422

Code: https://github.com/muellerjohannes/fisher-rao-GFs-LPs

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Gradient Flow — 85× in this paper · explained in 2 episodes
• Regularization — 30× in this paper · explained in 3 episodes
• Reinforcement Learning — 11× in this paper · explained in 4 episodes
• Actor — 6× in this paper · explained in 3 episodes
• Fisher Information — 5× in this paper · explained in 3 episodes
• Objective Function — 5× in this paper · explained in 2 episodes
• Generalization — 4× in this paper · explained in 13 episodes
• Convergence Guarantees — 3× in this paper · explained in 3 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Action Space — 2× in this paper · explained in 1 episode
• Optimal Transport — 2× in this paper · explained in 5 episodes
• Distribution Shift — 1× in this paper · explained in 6 episodes
• Regret — 1× in this paper · explained in 3 episodes
• Reinforcement Learning (RL) — 1× in this paper · explained in 25 episodes
• Reward Shaping — 1× in this paper · explained in 2 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes
• Sparsity — 1× in this paper · explained in 4 episodes

Sources

• GPT-4 Technical Report
• Linear Convergence for Natural Policy Gradient with Log-linear Policy Parametrization
• Dota 2 with Large Scale Deep Reinforcement Learning
• A Geometric Embedding Approach to Multiple Games and Multiple Populations
• Convergence and sample complexity of natural policy gradient primal-dual methods for constrained MDPs
• Actor-critic is implicitly biased towards high entropy optimal policies
• A Fisher-Rao gradient flow for entropy-regularised Markov decision processes in Polish spaces
• Optimal Rates of Convergence for Entropy Regularization in Discounted Markov Decision Processes
• A unified view of entropy-regularized Markov decision processes
• Proximal Policy Optimization Algorithms

Related papers

• Lions and Muons: Optimization via Stochastic Frank-Wolfe under Heavy-Tailed Noise
• Adam-HNAG: A Convergent Reformulation of Adam with Accelerated Rate
• Incremental Learning in Mirror Flows
• Online Control via Counterfactual Tracking
• Asynchronous Replanning in Two Population Linear Quadratic Mean Field Games: Information Requirements and Stability
• Petrov-Galerkin operator inference with application to stability-encouraging identification