A MACHINE LEARNING FRAMEWORK FOR HIGH-DIMENSIONAL MEAN FIELD GAMES AND REAL-TIME CONTROL
Abstract
This project develops a unified machine learning framework for the numerical solution of large-scale mean field games (MFG), optimal transport (OT), and optimal control (OC) problems. It combines rigorous mathematics with state-of-the-art advances in machine learning. They are aimed at the efficient solution of high-dimensional MFG and OT and real-time OC instances. Advances made in this project will open the door to applications of MFG, OT, and OC techniques to real-world challenges in science and engineering that are beyond reach with existing numerical methods. Our framework leverages the mathematical advances that have been made for MFG, OT, and OC in recent decades. Most importantly, we exploit thefact that high-dimensional Hamilton-Jacobi-Bellman (HJB) equations govern the solution of these problems. Our project develops Lagrangian PDE solvers and designs machine learning models that parameterize the HJB s solution. This combination leads to a mesh-free scheme, which helps us avoid the curse of dimensionality. The project consists of three research thrusts and one cross-cutting effort. The first research thrust will yield a framework that contains state-of-the-art machine learning and optimization algorithms, supports a wide range of modeling choices, and will determine guidelines for machine learning approaches to solve MFG, OT, and OC problems. The second research thrust will exploit optimal transport theory to obtain accurate and efficient solvers for high-dimensional problems. The third research thrust expands the framework to optimal control and develops active learning strategies for determining efficient closed-loop feedback controls that can be deployed in real-time applications. The supporting thrust develops and disseminates an open-source software package to accelerate the pace of further developments, supportreal-world applications, and ensure the reproducibility of our findings.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2021
- Source ID
- FA95502010372
Entities
People
- Lars Ruthotto
Organizations
- Air Force Office of Scientific Research
- Emory University
- United States Air Force