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Here, we observe that mean-field game (MFG) systems admit a two-player infinite-dimensional general-sum differential game formulation. We show that particular regimes of this game reduce to previously known variational principles.…

Analysis of PDEs · Mathematics 2018-04-25 Marco Cirant , 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

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

Motivated by the recent interests in asymmetric mean field games, this paper provides a general framework of Heterogeneous Mean Field Game (HMFG) that subsumes different formulations of graphon mean field games. The key feature of the HMFG…

Optimization and Control · Mathematics 2025-11-26 Bixing Qiao

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

Recent results of Ye and Hansen, Miltersen and Zwick show that policy iteration for one or two player (perfect information) zero-sum stochastic games, restricted to instances with a fixed discount rate, is strongly polynomial. We show that…

Optimization and Control · Mathematics 2013-10-21 Marianne Akian , Stéphane Gaubert

Non-cooperative and cooperative games with a very large number of players have many applications but remain generally intractable when the number of players increases. Introduced by Lasry and Lions, and Huang, Caines and Malham\'e, Mean…

We consider the problem of representing collective behavior of large populations and predicting the evolution of a population distribution over a discrete state space. A discrete time mean field game (MFG) is motivated as an interpretable…

Machine Learning · Computer Science 2018-04-24 Jiachen Yang , Xiaojing Ye , Rakshit Trivedi , Huan Xu , Hongyuan Zha

We consider stochastic control models with Borel spaces and universally measurable policies. For such models the standard policy iteration is known to have difficult measurability issues and cannot be carried out in general. We present a…

Optimization and Control · Mathematics 2016-02-26 Huizhen Yu , Dimitri P. Bertsekas

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 consider a dynamic traffic routing game over an urban road network involving a large number of drivers in which each driver selecting a particular route is subject to a penalty that is affine in the logarithm of the number of drivers…

Optimization and Control · Mathematics 2020-01-22 Takashi Tanaka , Ehsan Nekouei , Ali Reza Pedram , Karl Henrik Johansson

This paper employs a policy iteration reinforcement learning (RL) method to study continuous-time linear-quadratic mean-field control problems in infinite horizon. The drift and diffusion terms in the dynamics involve the states, the…

Optimization and Control · Mathematics 2024-11-05 Na Li , Xun Li , Zuo Quan Xu

Mean field control (MFC) problems have been introduced to study social optima in very large populations of strategic agents. The main idea is to consider an infinite population and to simplify the analysis by using a mean field…

Optimization and Control · Mathematics 2023-03-01 Sebastian Baudelet , Brieuc Frénais , Mathieu Laurière , Amal Machtalay , Yuchen Zhu

This thesis is going to give a gentle introduction to Mean Field Games. It aims to produce a coherent text beginning for simple notions of deterministic control theory progressively to current Mean Field Games theory. The framework…

Optimization and Control · Mathematics 2019-07-03 Athanasios Vasiliadis

Mean-field games (MFG) provide a statistical physics inspired modeling framework for decision making in large-populations of strategic, non-cooperative agents. Mathematically, these systems consist of a forward-backward in time system of…

Dynamical Systems · Mathematics 2024-05-10 Ali Akbar Rezaei Lori , Piyush Grover

We introduce Mean-Field Trust Region Policy Optimization (MF-TRPO), a novel algorithm designed to compute approximate Nash equilibria for ergodic Mean-Field Games (MFG) in finite state-action spaces. Building on the well-established…

Machine Learning · Statistics 2025-05-30 Antonio Ocello , Daniil Tiapkin , Lorenzo Mancini , Mathieu Laurière , Eric Moulines

We study the singular perturbation problem for mean field game systems with control of acceleration. For such a problem we analyze the behavior of solutions as the acceleration costs vanishes. In this setting the Hamiltonian fails to be…

Optimization and Control · Mathematics 2023-04-04 Cristian Mendico

Many multi-agent interaction scenarios can be naturally modeled as noncooperative games, where each agent's decisions depend on others' future actions. However, deploying game-theoretic planners for autonomous decision-making requires a…

Machine Learning · Computer Science 2026-01-05 Yash Jain , Xinjie Liu , Lasse Peters , David Fridovich-Keil , Ufuk Topcu

In this work, we study the contraction conditions of iterative algorithms for stationary and finite-horizon discrete-time regularized mean-field games (MFGs) with multiple populations, where each population only interacts with the state…

Optimization and Control · Mathematics 2026-05-26 Uğur Aydın , Tamer Başar

Competitive games involving thousands or even millions of players are prevalent in real-world contexts, such as transportation, communications, and computer networks. However, learning in these large-scale multi-agent environments presents…

Optimization and Control · Mathematics 2025-02-04 Batuhan Yardim , Semih Cayci , Niao He