Linear Supervision for Nonlinear, High-Dimensional Neural Control and Differential Games

William Sharpless, Zeyuan Feng, Somil Bansal, Sylvia Herbert
Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, PMLR 283:365-377, 2025.

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 this Paper

BibTeX
@InProceedings{pmlr-v283-sharpless25a, 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}, pages = {365--377}, year = {2025}, editor = {Ozay, Necmiye and Balzano, Laura and Panagou, Dimitra and Abate, Alessandro}, volume = {283}, series = {Proceedings of Machine Learning Research}, month = {04--06 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v283/main/assets/sharpless25a/sharpless25a.pdf}, url = {https://proceedings.mlr.press/v283/sharpless25a.html}, 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.} }
Endnote
%0 Conference Paper %T Linear Supervision for Nonlinear, High-Dimensional Neural Control and Differential Games %A William Sharpless %A Zeyuan Feng %A Somil Bansal %A Sylvia Herbert %B Proceedings of the 7th Annual Learning for Dynamics \& Control Conference %C Proceedings of Machine Learning Research %D 2025 %E Necmiye Ozay %E Laura Balzano %E Dimitra Panagou %E Alessandro Abate %F pmlr-v283-sharpless25a %I PMLR %P 365--377 %U https://proceedings.mlr.press/v283/sharpless25a.html %V 283 %X 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.
APA
Sharpless, W., Feng, Z., Bansal, S. & Herbert, S.. (2025). Linear Supervision for Nonlinear, High-Dimensional Neural Control and Differential Games. Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, in Proceedings of Machine Learning Research 283:365-377 Available from https://proceedings.mlr.press/v283/sharpless25a.html.

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