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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

We introduce a novel framework to model and solve mean-field game systems with nonlocal interactions. Our approach relies on kernel-based representations of mean-field interactions and feature-space expansions in the spirit of kernel…

Optimization and Control · Mathematics 2020-04-29 Siting Liu , Matthew Jacobs , Wuchen Li , Levon Nurbekyan , Stanley J. Osher

Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading…

Mathematical Finance · Quantitative Finance 2019-12-13 Philippe Casgrain , Sebastian Jaimungal

This paper presents recent results from Mean Field Game theory underlying the introduction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations…

Optimization and Control · Mathematics 2011-10-19 Olivier Guéant

Traditional mean-field game (MFG) solvers operate on an instance-by-instance basis, which becomes infeasible when many related problems must be solved (e.g., for seeking a robust description of the solution under perturbations of the…

Optimization and Control · Mathematics 2025-10-24 Dena Firoozi , Anastasis Kratsios , Xuwei Yang

We establish the convergence of the deep actor-critic reinforcement learning algorithm presented in [Angiuli et al., 2023a] in the setting of continuous state and action spaces with an infinite discrete-time horizon. This algorithm provides…

Optimization and Control · Mathematics 2025-11-11 Jean-Pierre Fouque , Mathieu Laurière , Mengrui Zhang

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

In this paper, we propose an initial value fomulation of the discrete mean field games on finite graphs (Graph MFG), and design a neural network based approach to solve it. Graph MFG describes infinite, non-cooperative and interactive…

Numerical Analysis · Mathematics 2026-04-08 Yaxin Feng , Yang Xiang , Haomin Zhou

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

We introduce Mean-Field Game (MFG) epidemiological models, in which immunity either wanes with time in a fully observable way or disappears instantaneously with no direct observation (making a previously recovered individual fully…

Optimization and Control · Mathematics 2026-04-08 Carlos Doebeli , Alexander Vladimirsky

This paper investigates a mean-field game (MFG) problem for mean-variance (MV) portfolio management, highlighting a new type of relative performance encoded by the peer-based risk aversion. Specifically, the risk aversion is formulated as a…

Mathematical Finance · Quantitative Finance 2026-05-26 Weilun Cheng , Zongxia Liang , Sheng Wang , Xiang Yu

In this work we study a constrained monotone inclusion involving the normal cone to a closed vector subspace and a priori information on primal solutions. We model this information by imposing that solutions belongs to the fixed point set…

Optimization and Control · Mathematics 2021-11-02 Luis Briceño-Arias , Julio Deride , Sergio López-Rivera , Francisco J. Silva

We propose and show the efficacy of a new method to address generic inverse problems. Inverse modeling is the task whereby one seeks to determine the control parameters of a natural system that produce a given set of observed measurements.…

Machine Learning · Computer Science 2023-08-15 Gregory P. Spell , Simiao Ren , Leslie M. Collins , Jordan M. Malof

This paper presents a novel model-free method to solve linear quadratic Gaussian mean field social control problems in the presence of multiplicative noise. The objective is to achieve a social optimum by solving two algebraic Riccati…

Optimization and Control · Mathematics 2025-11-11 Zhenhui Xu , Bing-Chang Wang , Tielong Shen

Entry-exit dynamics are crucial in modeling crowd movement. Here, we present a novel first-order, stationary mean-field game model on a bounded domain that accurately captures these dynamics. The interior dynamics of the system are governed…

Analysis of PDEs · Mathematics 2026-03-03 AbdulRahman M. Alharbi , Yuri Ashrafyan , Diogo Gomes

In this paper, we consider a mean field game model inspired by crowd motion in which several interacting populations evolving in $\mathbb R^d$ aim at reaching given target sets in minimal time. The movement of each agent is described by a…

Optimization and Control · Mathematics 2022-08-16 Saeed Sadeghi Arjmand , Guilherme Mazanti

We construct numerical approximations for Mean Field Games with fractional or nonlocal diffusions. The schemes are based on semi-Lagrangian approximations of the underlying control problems/games along with dual approximations of the…

Analysis of PDEs · Mathematics 2021-05-04 Indranil Chowdhury , Olav Ersland , Espen R. Jakobsen

For noncooperative games the mean field (MF) methodology provides decentralized strategies which yield Nash equilibria for large population systems in the asymptotic limit of an infinite (mass) population. The MF control laws use only the…

Optimization and Control · Mathematics 2012-10-22 Arman C. Kizilkale , Peter E. Caines

This paper investigates the control of a massive population of UAVs such as drones. The straightforward method of control of UAVs by considering the interactions among them to make a flock requires a huge inter-UAV communication which is…

Networking and Internet Architecture · Computer Science 2020-08-13 Hamid Shiri , Jihong Park , Mehdi Bennis

This paper presents a novel meta algorithm, Partition-Merge (PM), which takes existing centralized algorithms for graph computation and makes them distributed and faster. In a nutshell, PM divides the graph into small subgraphs using our…

Data Structures and Algorithms · Computer Science 2013-09-25 Vincent Blondel , Kyomin Jung , Pushmeet Kohli , Devavrat Shah