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arXiv · 2604.22138

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

Jhojan A. Rodriguez-Gil·César A. Uribe
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Abstract

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.

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Jhojan A. Rodriguez-Gil, César A. Uribe. 2026-04-24. Global Convergence of Policy Gradient Methods for ReLU Controllers in Linear Quadratic Regulation. https://arxiv.org/abs/2604.22138

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