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

TL;DR

This paper introduces a method that combines linear PDE solutions with deep learning to efficiently and accurately solve high-dimensional nonlinear control and differential game problems, outperforming traditional approaches.

Contribution

It presents two novel programs that integrate linear PDE supervision with neural networks, enhancing speed and accuracy in high-dimensional control tasks.

Findings

Improved speed and accuracy in 50-D differential game

Enhanced control performance in 10-D quadrotor problem

Linear supervision accelerates neural PDE solutions

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 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.