Geometry and convergence of natural policy gradient methods.

Area of Science:

• Reinforcement Learning
• Optimization Theory
• Machine Learning

Background:

• Markov decision processes (MDPs) are fundamental to reinforcement learning.
• Natural Policy Gradient (NPG) methods offer efficient policy optimization.
• Understanding convergence properties is crucial for algorithm reliability.

Purpose of the Study:

• To analyze the convergence of various NPG methods in infinite-horizon discounted MDPs.
• To establish global convergence guarantees and derive convergence rates.
• To connect NPG methods to gradient flows and Hessian geometries.

Main Methods:

• Formulating NPG trajectories as gradient flows with respect to Hessian geometries.
• Analyzing convergence rates for different NPG variants and reward functions.
• Interpreting discrete-time NPG as inexact Newton methods.

Main Results:

• Global convergence guarantees are established for a variety of NPG methods.
• Linear convergence rates are shown for NPG flows using entropy-based Hessian geometries.
• Sublinear convergence rates are derived for other convex geometries, and local quadratic convergence is demonstrated for regularized NPG.

Conclusions:

• The study provides a unified framework for understanding NPG convergence through Hessian geometries.
• The findings offer theoretical guarantees and practical insights for designing efficient reinforcement learning algorithms.
• The connection to gradient flows and Newton methods deepens the theoretical understanding of NPG.