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Real economies can be modeled as a sequential imperfect-information game with many heterogeneous agents, such as consumers, firms, and governments. Dynamic general equilibrium (DGE) models are often used for macroeconomic analysis in this…

Computer Science and Game Theory · Computer Science 2022-02-25 Michael Curry , Alexander Trott , Soham Phade , Yu Bai , Stephan Zheng

We present a new combined \textit{mean field control game} (MFCG) problem which can be interpreted as a competitive game between collaborating groups and its solution as a Nash equilibrium between groups. Players coordinate their strategies…

Optimization and Control · Mathematics 2023-02-16 Andrea Angiuli , Nils Detering , Jean-Pierre Fouque , Mathieu Lauriere , Jimin Lin

We address in this paper Reinforcement Learning (RL) among agents that are grouped into teams such that there is cooperation within each team but general-sum (non-zero sum) competition across different teams. To develop an RL method that…

Machine Learning · Computer Science 2025-02-11 Muhammad Aneeq uz Zaman , Alec Koppel , Mathieu Laurière , Tamer Başar

Designing suitable reward functions for numerous interacting intelligent agents is challenging in real-world applications. Inverse reinforcement learning (IRL) in mean field games (MFGs) offers a practical framework to infer reward…

Machine Learning · Computer Science 2025-09-05 Yang Chen , Xiao Lin , Bo Yan , Libo Zhang , Jiamou Liu , Neset Özkan Tan , Michael Witbrock

Mean Field Control (MFC) is a powerful approximation tool to solve large-scale Multi-Agent Reinforcement Learning (MARL) problems. However, the success of MFC relies on the presumption that given the local states and actions of all the…

Machine Learning · Computer Science 2023-05-30 Washim Uddin Mondal , Vaneet Aggarwal , Satish V. Ukkusuri

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

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

The capability to learn and adapt to changes in the driving environment is crucial for developing autonomous driving systems that are scalable beyond geo-fenced operational design domains. Deep Reinforcement Learning (RL) provides a…

Machine Learning · Computer Science 2019-11-12 Praveen Palanisamy

Scalability remains a challenge in multi-agent reinforcement learning and is currently under active research. A framework named mean-field reinforcement learning (MFRL) could alleviate the scalability problem by employing the Mean Field…

Artificial Intelligence · Computer Science 2025-02-21 Hao Ma , Zhiqiang Pu , Yi Pan , Boyin Liu , Junlong Gao , Zhenyu Guo

Mean-field reinforcement learning has become a popular theoretical framework for efficiently approximating large-scale multi-agent reinforcement learning (MARL) problems exhibiting symmetry. However, questions remain regarding the…

Computer Science and Game Theory · Computer Science 2024-02-09 Batuhan Yardim , Artur Goldman , Niao He

Learning by experience in Multi-Agent Systems (MAS) is a difficult and exciting task, due to the lack of stationarity of the environment, whose dynamics evolves as the population learns. In order to design scalable algorithms for systems…

Optimization and Control · Mathematics 2020-02-24 Romuald Elie , Julien Pérolat , Mathieu Laurière , Matthieu Geist , Olivier Pietquin

Multi-agent reinforcement learning (MARL) remains difficult to scale to many agents. Recent MARL using Mean Field Control (MFC) provides a tractable and rigorous approach to otherwise difficult cooperative MARL. However, the strict MFC…

Machine Learning · Computer Science 2024-05-09 Kai Cui , Christian Fabian , Anam Tahir , Heinz Koeppl

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

Multi-agent deep reinforcement learning makes optimal decisions dependent on system states observed by agents, but any uncertainty on the observations may mislead agents to take wrong actions. The Mean-Field Actor-Critic reinforcement…

Machine Learning · Computer Science 2023-06-01 Ziyuan Zhou , Guanjun Liu

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

Existing multi-agent reinforcement learning methods are limited typically to a small number of agents. When the agent number increases largely, the learning becomes intractable due to the curse of the dimensionality and the exponential…

Multiagent Systems · Computer Science 2020-12-16 Yaodong Yang , Rui Luo , Minne Li , Ming Zhou , Weinan Zhang , Jun Wang

This paper explores the use of Maximum Causal Entropy Inverse Reinforcement Learning (IRL) within the context of discrete-time stationary Mean-Field Games (MFGs) characterized by finite state spaces and an infinite-horizon,…

Systems and Control · Electrical Eng. & Systems 2025-07-22 Berkay Anahtarci , Can Deha Kariksiz , Naci Saldi

We propose a new model, independent linear Markov game, for multi-agent reinforcement learning with a large state space and a large number of agents. This is a class of Markov games with independent linear function approximation, where each…

Machine Learning · Computer Science 2023-06-23 Qiwen Cui , Kaiqing Zhang , Simon S. Du

While the topic of mean-field games (MFGs) has a relatively long history, heretofore there has been limited work concerning algorithms for the computation of equilibrium control policies. In this paper, we develop a computable policy…

Systems and Control · Electrical Eng. & Systems 2020-04-07 Muhammad Aneeq uz Zaman , Kaiqing Zhang , Erik Miehling , Tamer Başar

This paper studies the discrete-time linear-quadratic-Gaussian mean field (MF) social control problem in an infinite horizon, where the dynamics of all agents are unknown. The objective is to design a reinforcement learning (RL) algorithm…

Optimization and Control · Mathematics 2025-12-05 Hanfang Zhang , Bing-Chang Wang , Shuo Chen