# Policy Gradient Converges to the Globally Optimal Policy for Nearly Linear-Quadratic Regulators

arXiv: https://arxiv.org/abs/2303.08431 · HTML: https://mlsanity.com/paper/2303.08431/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 56 references that are in the map.
- First posted on arXiv 15 Mar 2023.

## Builds on (most cited first, 23 of 23)

- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [End-to-End Training of Deep Visuomotor Policies](https://mlsanity.com/paper/1504.00702/) (2015)
- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [Fast Global Convergence of Natural Policy Gradient Methods with Entropy Regularization](https://mlsanity.com/paper/2007.06558/) (2020)
- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Neural Policy Gradient Methods: Global Optimality and Rates of Convergence](https://mlsanity.com/paper/1909.01150/) (2019)
- [On the Convergence Rates of Policy Gradient Methods](https://mlsanity.com/paper/2201.07443/) (2022)
- [Variational Policy Gradient Method for Reinforcement Learning with General Utilities](https://mlsanity.com/paper/2007.02151/) (2020)
- [An Improved Analysis of (Variance-Reduced) Policy Gradient and Natural Policy Gradient Methods](https://mlsanity.com/paper/2211.07937/) (2022)
- [Derivative-Free Methods for Policy Optimization: Guarantees for Linear Quadratic Systems](https://mlsanity.com/paper/1812.08305/) (2018)
- [Stochastic Policy Gradient Methods: Improved Sample Complexity for Fisher-non-degenerate Policies](https://mlsanity.com/paper/2302.01734/) (2023)
- [On Linear Convergence of Policy Gradient Methods for Finite MDPs](https://mlsanity.com/paper/2007.11120/) (2020)
- [Policy Gradient Methods for the Noisy Linear Quadratic Regulator over a Finite Horizon](https://mlsanity.com/paper/2011.10300/) (2020)
- [Policy Optimization for H2 Linear Control with H_∞ Robustness Guarantee: Implicit Regularization and Global Convergence](https://mlsanity.com/paper/1910.09496/) (2019)
- [LQR through the Lens of First Order Methods: Discrete-time Case](https://mlsanity.com/paper/1907.08921/) (2019)
- [Single-Timescale Actor-Critic Provably Finds Globally Optimal Policy](https://mlsanity.com/paper/2008.00483/) (2020)
- [Feedback Linearization based on Gaussian Processes with event-triggered Online Learning](https://mlsanity.com/paper/1911.06565/) (2019)
- [Doubly Robust Off-Policy Actor-Critic: Convergence and Optimality](https://mlsanity.com/paper/2102.11866/) (2021)
- [Exploration-exploitation trade-off for continuous-time episodic reinforcement learning with linear-convex models](https://mlsanity.com/paper/2112.10264/) (2021)
- [Convergence Guarantees of Policy Optimization Methods for Markovian Jump Linear Systems](https://mlsanity.com/paper/2002.04090/) (2020)
- [On the Analysis of Model-free Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/2007.03861/) (2020)
- [Optimal scheduling of entropy regulariser for continuous-time linear-quadratic reinforcement learning](https://mlsanity.com/paper/2208.04466/) (2022)

## Built on by (most cited first, 5 of 5)

- [A Fisher-Rao gradient flow for entropy-regularised Markov decision processes in Polish spaces](https://mlsanity.com/paper/2310.02951/) (2023)
- [Stochastic Control for Fine-tuning Diffusion Models: Optimality, Regularity, and Convergence](https://mlsanity.com/paper/2412.18164/) (2024)
- [Fast Policy Learning for Linear Quadratic Control with Entropy Regularization](https://mlsanity.com/paper/2311.14168/) (2023)
- [Learning Zero-Sum Linear Quadratic Games with Improved Sample Complexity and Last-Iterate Convergence](https://mlsanity.com/paper/2309.04272/) (2023)
- [Convergence Guarantees of Model-free Policy Gradient Methods for LQR with Stochastic Data](https://mlsanity.com/paper/2502.19977/) (2025)

## Abstract (arXiv)

Nonlinear control systems with partial information to the decision maker are prevalent in a variety of applications. As a step toward studying such nonlinear systems, this work explores reinforcement learning methods for finding the optimal policy in the nearly linear-quadratic regulator systems. In particular, we consider a dynamic system that combines linear and nonlinear components, and is governed by a policy with the same structure. Assuming that the nonlinear component comprises kernels with small Lipschitz coefficients, we characterize the optimization landscape of the cost function. Although the cost function is nonconvex in general, we establish the local strong convexity and smoothness in the vicinity of the global optimizer. Additionally, we propose an initialization mechanism to leverage these properties. Building on the developments, we design a policy gradient algorithm that is guaranteed to converge to the globally optimal policy with a linear rate.