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We investigate the global numerical approximation of a class of extended mean field control problems (MFC), where the dynamics and costs depend on the joint distribution of the state and the control. We propose a framework to approximate…

Optimization and Control · Mathematics 2026-03-23 Athena Picarelli , Marco Scaratti , Jonathan Tam

Conventional affine formation control (AFC) empowers a network of agents with flexible but collective motions - a potential which has not yet been exploited for large-scale swarms. One of the key bottlenecks lies in the design of an…

Systems and Control · Electrical Eng. & Systems 2026-03-31 Zhonggang Li , Geert Leus , Raj Thilak Rajan

Learning in multi-agent systems is highly challenging due to several factors including the non-stationarity introduced by agents' interactions and the combinatorial nature of their state and action spaces. In particular, we consider the…

Machine Learning · Statistics 2023-05-10 Barna Pásztor , Ilija Bogunovic , Andreas Krause

In this paper we consider a mean field optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a…

Analysis of PDEs · Mathematics 2019-09-25 Jose A. Carrillo , Edgard A. Pimentel , Vardan K. Voskanyan

We develop a scalable algorithm for mean field control problems with kernel interactions by combining particle system simulations with random Fourier feature approximations. The method replaces the quadratic-cost kernel evaluations by…

Optimization and Control · Mathematics 2026-05-25 Zhongyuan Cao , Kaustav Das , Nicolas Langrené , Mathieu Laurière

Reinforcement learning is a powerful tool to learn the optimal policy of possibly multiple agents by interacting with the environment. As the number of agents grow to be very large, the system can be approximated by a mean-field problem.…

Optimization and Control · Mathematics 2020-08-18 Weichen Wang , Jiequn Han , Zhuoran Yang , Zhaoran Wang

In recent years, reinforcement learning and its multi-agent analogue have achieved great success in solving various complex control problems. However, multi-agent reinforcement learning remains challenging both in its theoretical analysis…

Robotics · Computer Science 2023-02-10 Kai Cui , Mengguang Li , Christian Fabian , Heinz Koeppl

In this paper, we introduce a new class of potential fields, i.e., meta navigation functions (MNFs) to coordinate multi-agent systems. Thanks to the MNF formulation, agents can contribute to each other's coordination via partial and/or…

Robotics · Computer Science 2022-10-05 Matin Macktoobian , Guillaume Ferdinand Duc

Recent reinforcement learning (RL) methods have achieved success in various domains. However, multi-agent RL (MARL) remains a challenge in terms of decentralization, partial observability and scalability to many agents. Meanwhile,…

Machine Learning · Computer Science 2024-02-26 Kai Cui , Sascha Hauck , Christian Fabian , Heinz Koeppl

This paper deals with the derivation of the mean-field limit for multi-agent systems on a large class of sparse graphs. More specifically, the case of non-exchangeable multi-agent systems consisting of non-identical agents is addressed. The…

Probability · Mathematics 2025-11-21 Pierre-Emmanuel Jabin , David Poyato , Juan Soler

We introduce the concept of {\it mean-field optimal control} which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional…

Optimization and Control · Mathematics 2019-02-20 Massimo Fornasier , Francesco Solombrino

When controlling multi-agent systems, the trade-off between performance and scalability is a major challenge. Here, we address this difficulty by using mean field games (MFGs), which is a framework that deduces the macroscopic dynamics…

Optimization and Control · Mathematics 2021-08-06 Daisuke Inoue , Yuji Ito , Takahito Kashiwabara , Norikazu Saito , Hiroaki Yoshida

We investigate reinforcement learning in the setting of Markov decision processes for a large number of exchangeable agents interacting in a mean field manner. Applications include, for example, the control of a large number of robots…

Optimization and Control · Mathematics 2025-04-30 René Carmona , Mathieu Laurière , Zongjun Tan

Many applications involving multi-agent systems require fulfilling safety constraints. Control barrier functions offer a systematic framework to enforce forward invariance of safety sets. Recent work extended this paradigm to mean-field…

Systems and Control · Electrical Eng. & Systems 2026-03-20 Cinzia Tomaselli , Gian Carlo Maffettone , Samy Wu Fung , Levon Nurbekyan , Mario di Bernardo

Mean field games (MFG) and mean field control (MFC) are critical classes of multi-agent models for efficient analysis of massive populations of interacting agents. Their areas of application span topics in economics, finance, game theory,…

Machine Learning · Computer Science 2022-06-08 Lars Ruthotto , Stanley Osher , Wuchen Li , Levon Nurbekyan , Samy Wu Fung

In this work we are interested in the mean-field formulation of kinetic models under control actions where the control is formulated through a model predictive control strategy (MPC) with varying horizon. The relation between the (usually…

Optimization and Control · Mathematics 2015-11-30 Michael Herty , Mattia Zanella

Methods like multi-agent reinforcement learning struggle to scale with growing population size. Mean-field games (MFGs) are a game-theoretic approach that can circumvent this by finding a solution for an abstract infinite population, which…

Multiagent Systems · Computer Science 2025-12-23 Patrick Benjamin , Alessandro Abate

We study the linear-quadratic control problem for a class of non-exchangeable mean-field systems, which model large populations of heterogeneous interacting agents. We explicitly characterize the optimal control in terms of a new…

Optimization and Control · Mathematics 2025-12-30 Anna de Crescenzo , Filippo de Feo , Huyên Pham

Mean field equilibrium (MFE) has emerged as a computationally tractable solution concept for large dynamic games. However, computing MFE remains challenging due to nonlinearities and the absence of contraction properties, limiting its…

Theoretical Economics · Economics 2025-06-23 Bar Light

Coordinating large populations of autonomous agents, such as UAV swarms or satellite constellations, poses significant computational challenges for traditional multi-agent control methods. This paper introduces a new optimization framework…

Optimization and Control · Mathematics 2026-03-18 Di Yu , Sixiong You , Chaoying Pei