Global Convergence of Policy Gradient Methods for ReLU Controllers in Linear Quadratic Regulation
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911619866427392 |
|---|---|
| author | Rodriguez-Gil, Jhojan A. Uribe, César A. |
| author_facet | Rodriguez-Gil, Jhojan A. Uribe, César A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22138 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global Convergence of Policy Gradient Methods for ReLU Controllers in Linear Quadratic Regulation Rodriguez-Gil, Jhojan A. Uribe, César A. Optimization and Control Systems and Control 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. |
| title | Global Convergence of Policy Gradient Methods for ReLU Controllers in Linear Quadratic Regulation |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2604.22138 |