# Global Convergence of Policy Gradient Methods for ReLU Controllers in Linear Quadratic Regulation

arXiv: https://arxiv.org/abs/2604.22138 · HTML: https://mlsanity.com/paper/2604.22138/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 13 of its 17 references that are in the map.
- First posted on arXiv 24 Apr 2026.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

## Builds on (most cited first, 13 of 13)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Gradient Descent Provably Optimizes Over-parameterized Neural Networks](https://mlsanity.com/paper/1810.02054/) (2018)
- [Gradient Descent Finds Global Minima of Deep Neural Networks](https://mlsanity.com/paper/1811.03804/) (2018)
- [On the Optimization of Deep Networks: Implicit Acceleration by Overparameterization](https://mlsanity.com/paper/1802.06509/) (2018)
- [Global Convergence of Policy Gradient Methods for the Linear Quadratic Regulator](https://mlsanity.com/paper/1801.05039/) (2018)
- [Algorithmic Regularization in Learning Deep Homogeneous Models: Layers are Automatically Balanced](https://mlsanity.com/paper/1806.00900/) (2018)
- [Neural Policy Gradient Methods: Global Optimality and Rates of Convergence](https://mlsanity.com/paper/1909.01150/) (2019)
- [Global Optimality Guarantees For Policy Gradient Methods](https://mlsanity.com/paper/1906.01786/) (2019)
- [Derivative-Free Methods for Policy Optimization: Guarantees for Linear Quadratic Systems](https://mlsanity.com/paper/1812.08305/) (2018)
- [Neural System Level Synthesis: Learning over All Stabilizing Policies for Nonlinear Systems](https://mlsanity.com/paper/2203.11812/) (2022)
- [Sample Complexity of the Linear Quadratic Regulator: A Reinforcement Learning Lens](https://mlsanity.com/paper/2404.10851/) (2024)
- [Convergence Analysis of Gradient Flow for Overparameterized LQR Formulations](https://mlsanity.com/paper/2408.15456/) (2024)
- [On the (almost) Global Exponential Convergence of the Overparameterized Policy Optimization for the LQR Problem](https://mlsanity.com/paper/2510.02140/) (2025)

## Abstract (arXiv)

We study the convergence of model-based policy gradient for the deterministic, scalar, discounted linear-quadratic regulator when the controller is an overparameterized one-hidden-layer ReLU network without biases. Although the optimal LQR controller is linear, neural parameterization creates a redundant nonconvex weight space with a possibly asymmetric piecewise-linear controller. We show that this structure can still be analyzed exactly through the two effective gains induced on the positive and negative half-lines. Under suitable random initialization, sufficient width, and a small step size, the model-based policy gradient remains stable, decreases the cost geometrically, and drives the effective gains to the unique optimal scalar LQR gain with high probability.