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

Fuente: arXiv
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Main Authors: Sharpless, William, Feng, Zeyuan, Bansal, Somil, Herbert, Sylvia
Format: Preprint
Published: 2024
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author Sharpless, William
Feng, Zeyuan
Bansal, Somil
Herbert, Sylvia
author_facet Sharpless, William
Feng, Zeyuan
Bansal, Somil
Herbert, Sylvia
contents 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 linear solutions to the partial differential equation (PDE) arising in the problem to accelerate and improve learned value functions for guidance in high-dimensional, 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.
format Preprint
id arxiv_https___arxiv_org_abs_2412_02033
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Linear Supervision for Nonlinear, High-Dimensional Neural Control and Differential Games
Sharpless, William
Feng, Zeyuan
Bansal, Somil
Herbert, Sylvia
Optimization and Control
Systems and Control
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 linear solutions to the partial differential equation (PDE) arising in the problem to accelerate and improve learned value functions for guidance in high-dimensional, 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.
title Linear Supervision for Nonlinear, High-Dimensional Neural Control and Differential Games
topic Optimization and Control
Systems and Control
url https://arxiv.org/abs/2412.02033