Convexifying Mean-Field Control: An Occupation-Measure And Frank-Wolfe Approach

Author

• Di Yu
• Sixiong You
• Chaoying Pei, Missouri University of Science and TechnologyFollow

Abstract

Large-scale robotic swarms motivate the use of mean-field control (MFC). Classical partial differential equation (PDE)-based formulations provide a principled framework but can become computationally challenging in higher dimensions, whereas machine learning achieves scalability at the cost of approximation and guarantees. In this work, we establish an optimization-based framework that lifts the MFC problem into the space of occupation measures, resulting in a convex relaxation formulated as an optimization over measures. The resulting problem is solved using a Frank-Wolfe (FW) algorithm in the measure space, with each iteration reduced to a tractable optimal control problem. This approach retains the O(1/k) convergence rate of FW, avoids discretization of the state space, and naturally incorporates interaction and safety constraints. Numerical experiments demonstrate agreement with analytic and PDE-based baselines in two dimensions and show that the method scales to three-dimensional environments with multiple obstacles, where standard grid-based PDE solvers become impractical. A full 3D instance with ten obstacles is solved in minutes on a standard workstation, underscoring the practicality and scalability of the proposed framework.

Recommended Citation

D. Yu et al., "Convexifying Mean-Field Control: An Occupation-Measure And Frank-Wolfe Approach," Proceedings of the American Control Conference, pp. 1504 - 1510, Institute of Electrical and Electronics Engineers, Jan 2026.

The definitive version is available at https://doi.org/10.48550/arXiv.2607.22678

Department(s)

Mechanical and Aerospace Engineering

International Standard Book Number (ISBN)

979-8-3315-9381-0; 979-8-3315-9382-7

International Standard Serial Number (ISSN)

0743-1619

Document Type

Article - Conference proceedings

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2026 Institute of Electrical and Electronics Engineers, All rights reserved.

Publication Date

01 Jan 2026