English
Related papers

Related papers: A Machine Learning Framework for Solving High-Dime…

200 papers

This paper proposes an efficient computational framework for longitudinal velocity control of a large number of autonomous vehicles (AVs) and develops a traffic flow theory for AVs. Instead of hypothesizing explicitly how AVs drive, our…

Optimization and Control · Mathematics 2020-12-14 Kuang Huang , Xuan Di , Qiang Du , Xi Chen

We present APAC-Net, an alternating population and agent control neural network for solving stochastic mean field games (MFGs). Our algorithm is geared toward high-dimensional instances of MFGs that are beyond reach with existing solution…

Machine Learning · Computer Science 2023-07-17 Alex Tong Lin , Samy Wu Fung , Wuchen Li , Levon Nurbekyan , Stanley J. Osher

We propose a control-theoretic framework for evolutionary clustering based on Mean Field Games (MFG). Moving beyond static or heuristic approaches, we formulate the problem as a population dynamics game governed by a coupled…

Numerical Analysis · Mathematics 2026-03-31 Alessio Basti , Fabio Camilli , Adriano Festa

We present a method enabling a large number of agents to learn how to flock, which is a natural behavior observed in large populations of animals. This problem has drawn a lot of interest but requires many structural assumptions and is…

Multiagent Systems · Computer Science 2021-05-18 Sarah Perrin , Mathieu Laurière , Julien Pérolat , Matthieu Geist , Romuald Élie , Olivier Pietquin

In this paper, we study the fundamental statistical efficiency of Reinforcement Learning in Mean-Field Control (MFC) and Mean-Field Game (MFG) with general model-based function approximation. We introduce a new concept called Mean-Field…

Machine Learning · Computer Science 2024-10-04 Jiawei Huang , Batuhan Yardim , Niao He

In this paper, we propose several approaches to learn the optimal population-dependent controls in order to solve mean field control problems (MFC). Such policies enable us to solve MFC problems with forms of common noises at a level of…

Optimization and Control · Mathematics 2023-11-21 Gokce Dayanikli , Mathieu Lauriere , Jiacheng Zhang

In this note, we develop Fourier approximation methods for the solutions of first-order nonlocal mean-field games (MFG) systems. Using Fourier expansion techniques, we approximate a given MFG system by a simpler one that is equivalent to a…

Analysis of PDEs · Mathematics 2019-01-21 Levon Nurbekyan , Joao Saude

Mean Field Game (MFG) models implicitly assume "rational expectations", meaning that the heterogeneous agents being modeled correctly know all relevant transition probabilities for the complex system they inhabit. When there is common…

Analysis of PDEs · Mathematics 2026-02-26 Benjamin Moll , Lenya Ryzhik

Mean field games (MFGs) offer a powerful framework for modeling large-scale multi-agent systems. This paper addresses MFGs formulated in continuous time with discrete state spaces, where agents' dynamics are governed by continuous-time…

Computer Science and Game Theory · Computer Science 2026-02-27 Yannick Eich , Christian Fabian , Kai Cui , Heinz Koeppl

This manuscript discusses planning problems for first- and second-order one-dimensional mean-field games (MFGs). These games are comprised of a Hamilton-Jacobi equation coupled with a Fokker-Planck equation. Applying Poincar\'e's Lemma to…

Analysis of PDEs · Mathematics 2021-04-27 Tigran Bakaryan , Rita Ferreira , Diogo Gomes

Mean-field games (MFGs) have shown strong modeling capabilities for large systems in various fields, driving growth in computational methods for mean-field game problems. However, high order methods have not been thoroughly investigated. In…

Numerical Analysis · Mathematics 2023-08-16 Guosheng Fu , Siting Liu , Stanley Osher , Wuchen Li

We study a Mean Field Games (MFG) system in a real, separable infinite dimensional Hilbert space. The system consists of a second order parabolic type equation, called Hamilton-Jacobi-Bellman (HJB) equation in the paper, coupled with a…

Analysis of PDEs · Mathematics 2025-09-05 Salvatore Federico , Fausto Gozzi , Andrzej Święch

In this work, we consider a novel inverse problem in mean-field games (MFG). We aim to recover the MFG model parameters that govern the underlying interactions among the population based on a limited set of noisy partial observations of the…

Numerical Analysis · Mathematics 2022-04-12 Yat Tin Chow , Samy Wu Fung , Siting Liu , Levon Nurbekyan , Stanley Osher

We propose an efficient solution approach for high-dimensional nonlocal mean-field game (MFG) systems based on the Monte Carlo approximation of interaction kernels via random features. We avoid costly space-discretizations of interaction…

Numerical Analysis · Mathematics 2022-07-26 Sudhanshu Agrawal , Wonjun Lee , Samy Wu Fung , Levon Nurbekyan

Mean-Field Control (MFC) has recently been proven to be a scalable tool to approximately solve large-scale multi-agent reinforcement learning (MARL) problems. However, these studies are typically limited to unconstrained cumulative reward…

Machine Learning · Computer Science 2024-09-11 Washim Uddin Mondal , Vaneet Aggarwal , Satish V. Ukkusuri

Understanding and modeling pedestrian dynamics in dense crowds is a complex yet essential aspect of crowd management and urban planning. In this work, we investigate the dynamics of a dense crowd crossed by a cylindrical intruder using a…

Physics and Society · Physics 2024-05-29 Matteo Butano , Cécile Appert-Rolland , Denis Ullmo

Mean Field Games (MFG) theory describes strategic interactions in differential games with a large number of small and indistinguishable players. Traditionally, the players' control impacts only the drift term in the system's dynamics,…

Analysis of PDEs · Mathematics 2024-07-31 Vincenzo Ignazio , Michele Ricciardi

This paper concerns a Mean Field Game (MFG) system related to a Nash type equilibrium for dynamical games associated to large populations. One shows that the MFG system may be viewed as the Euler-Lagrange system for an optimal control…

Optimization and Control · Mathematics 2025-03-21 Stefana-Lucia Anita

The intersection of Mean Field Games (MFGs) and Reinforcement Learning (RL) has fostered a growing family of algorithms designed to solve large-scale multi-agent systems. However, the field currently lacks a standardized evaluation…

Machine Learning · Computer Science 2026-02-16 Lorenzo Magnino , Jiacheng Shen , Matthieu Geist , Olivier Pietquin , Mathieu Laurière

We study infinite horizon discounted Mean Field Control (MFC) problems with common noise through the lens of Mean Field Markov Decision Processes (MFMDP). We allow the agents to use actions that are randomized not only at the individual…

Optimization and Control · Mathematics 2021-10-14 René Carmona , Mathieu Laurière , Zongjun Tan