Linear Supervision for Nonlinear, High-Dimensional Neural Control and Differential Games
Abstract
As the dimension of a system increases, traditional methods for control and differential games rapidly become intractable, making the design of safe autonomous agents challenging in complex or team settings. Deep-learning approaches avoid discretization and yield numerous successes in robotics and autonomy, but at a higher dimensional limit, accuracy falls as sampling becomes less efficient. We propose using rapidly generated \textit{linear} solutions to the partial differential equation (PDE) arising in the problem to accelerate and improve learned value functions for guidance in high-dimensional, \textit{nonlinear} problems. We define two programs that combine supervision of the linear solution with a standard PDE loss. We demonstrate that these programs offer improvements in speed and accuracy in both a 50-D differential game problem and a 10-D quadrotor control problem.
Cite
Text
Sharpless et al. "Linear Supervision for Nonlinear, High-Dimensional Neural Control and Differential Games." Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, 2025.Markdown
[Sharpless et al. "Linear Supervision for Nonlinear, High-Dimensional Neural Control and Differential Games." Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, 2025.](https://mlanthology.org/l4dc/2025/sharpless2025l4dc-linear/)BibTeX
@inproceedings{sharpless2025l4dc-linear,
title = {{Linear Supervision for Nonlinear, High-Dimensional Neural Control and Differential Games}},
author = {Sharpless, William and Feng, Zeyuan and Bansal, Somil and Herbert, Sylvia},
booktitle = {Proceedings of the 7th Annual Learning for Dynamics \& Control Conference},
year = {2025},
pages = {365-377},
volume = {283},
url = {https://mlanthology.org/l4dc/2025/sharpless2025l4dc-linear/}
}