New Convergence Guarantees for Natural Policy Gradient Algorithm

Asha Barua, Sajad Khodadadian· July 28, 2026 View original

Summary

This paper presents the first finite-time convergence guarantees for the Natural Policy Gradient (NPG) algorithm in finite-horizon Markov Decision Processes, analyzing both constant and increasing step size regimes and demonstrating sublinear and linear convergence rates.

The Natural Policy Gradient (NPG) algorithm is a foundational method in Reinforcement Learning, underpinning popular algorithms like TRPO and PPO, which have shown strong empirical success. This research delves into the theoretical underpinnings of exact NPG within the context of finite-horizon Markov Decision Processes (MDPs) where dynamics and transition kernels are horizon-dependent. The paper provides the first finite-time convergence guarantees for NPG in this specific setting. It examines two step size strategies: a constant step size and an increasing step size. For a constant step size, the NPG algorithm is proven to converge sublinearly at a rate of O(H²/t) after `t` iterations, where `H` is the horizon length. This sublinear rate also extends to linear MDPs under specific conditions. Crucially, with increasing step sizes, the research demonstrates that NPG can achieve a linear convergence rate of O((1 - 1/ϑρ)^t) for a problem-dependent constant ϑρ > 1. A specific horizon-only robust schedule for the step size is shown to attain this geometric rate. These theoretical guarantees provide a deeper understanding of NPG's performance characteristics.

Why it matters

For AI researchers and practitioners working with reinforcement learning, these new theoretical convergence guarantees for NPG provide a stronger foundation for understanding, designing, and optimizing RL algorithms, potentially leading to more stable and efficient training.

How to implement this in your domain

  1. 1Review the theoretical guarantees to inform the selection of step-size schedules in NPG-based RL implementations.
  2. 2Experiment with increasing step-size schedules in custom RL environments to potentially achieve faster convergence.
  3. 3Apply the insights to fine-tune hyperparameters for TRPO and PPO algorithms in practical applications.
  4. 4Consider the implications of horizon length on convergence rates when designing RL agents for finite-horizon tasks.

Who benefits

RoboticsAutonomous SystemsGamingLogisticsFinance

Key takeaways

  • NPG now has finite-time convergence guarantees for finite-horizon MDPs.
  • Constant step sizes lead to sublinear convergence (O(H²/t)).
  • Increasing step sizes can achieve linear convergence (O((1 - 1/ϑρ)^t)).
  • These theoretical insights can guide more effective RL algorithm design.

Original post by Asha Barua, Sajad Khodadadian

"arXiv:2607.22982v1 Announce Type: new Abstract: Natural Policy Gradient (NPG) is a well-established Reinforcement Learning algorithm that underlies widely used methods such as Trust Region Policy Optimization and Proximal Policy Optimization, both of which have demonstrated stron…"

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Originally posted by Asha Barua, Sajad Khodadadian on X · view source

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