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We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within…

Optimization and Control · Mathematics 2026-01-21 Zongxia Liang , Zhou Zhou , Yaqi Zhuang , Bin Zou

In this book, we present a curated collection of existing results on inverse problems for Mean Field Games (MFGs), a cutting-edge and rapidly evolving field of research. Our aim is to provide fresh insights, novel perspectives, and a…

Analysis of PDEs · Mathematics 2025-03-20 Hongyu Liu , Catharine W. K. Lo , Shen Zhang

Mean-field control (MFC) problems aim to find the optimal policy to control massive populations of interacting agents. These problems are crucial in areas such as economics, physics, and biology. We consider the non-local setting, where the…

Optimization and Control · Mathematics 2024-05-20 Alexander Vidal , Samy Wu Fung , Stanley Osher , Luis Tenorio , Levon Nurbekyan

Conventional stochastic control methods have several limitations. They focus on optimizing the average performance and, in some cases, performance variability; however, their problem settings still require an explicit specification of the…

Optimization and Control · Mathematics 2026-03-12 Yuma Shida , Yuji Ito

We use the Markov chain approximation method to construct approximations for the solution of the mean field game (MFG) with reflecting barriers studied in Bayraktar, Budhiraja, and Cohen (2017). The MFG is formulated in terms of a…

Optimization and Control · Mathematics 2018-08-28 Erhan Bayraktar , Amarjit Budhiraja , Asaf Cohen

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

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

For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…

Probability · Mathematics 2025-11-03 Nicolai Jurek Gerber , Franca Hoffmann , Urbain Vaes

Integrating renewable energy into the power grid while balancing supply and demand is a complex issue, given its intermittent nature. Demand side management (DSM) offers solutions to this challenge. We propose a new method for DSM, in…

Optimization and Control · Mathematics 2023-05-26 Bianca Marin Moreno , Margaux Brégère , Pierre Gaillard , Nadia Oudjane

We propose two algorithms for the solution of the optimal control of ergodic McKean-Vlasov dynamics. Both algorithms are based on approximations of the theoretical solutions by neural networks, the latter being characterized by their…

Optimization and Control · Mathematics 2021-03-30 René Carmona , Mathieu Laurière

In this article, we provide an original systematic global-in-time analysis of mean field type control problems on $\mathbb{R}^n$ with generic cost functionals by the modified approach but not the same, firstly proposed in [7], as the…

Optimization and Control · Mathematics 2023-05-09 Alain Bensoussan , Ho Man Tai , Sheung Chi Phillip Yam

We study sparse optimal control of a non-local continuity equation, where the goal is to steer a distribution via finitely many controllable agents or actuators. This model arises naturally in mean-field multi-agent systems and takes the…

Optimization and Control · Mathematics 2026-03-03 Enrico Sartor , Florian Dörfler , Nicolas Lanzetti

Mean field games are studied in the framework of controlled martingale problems, and general existence theorems are proven in which the equilibrium control is Markovian. The framework is flexible enough to include degenerate volatility,…

Probability · Mathematics 2015-04-09 Daniel Lacker

This paper studies mean field games for multi-agent systems with control-dependent multiplicative noises. For the general systems with nonuniform agents, we obtain a set of decentralized strategies by solving an auxiliary limiting optimal…

Optimization and Control · Mathematics 2019-06-10 Bing-Chang Wang , Yuan-Hua Ni , Huanshui Zhang

In this paper, we introduce discrete-time linear mean-field games subject to an infinite-horizon discounted-cost optimality criterion. The state space of a generic agent is a compact Borel space. At every time, each agent is randomly…

Systems and Control · Electrical Eng. & Systems 2023-01-18 Naci Saldi

This paper is concerned with a new class of mean-field games which involve a finite number of agents. Necessary and sufficient conditions are obtained for the existence of the decentralized open-loop Nash equilibrium in terms of…

Optimization and Control · Mathematics 2022-06-14 Bing-Chang Wang , Huanshui Zhang , Minyue Fu , Yong Liang

Mean-field games (MFGs) are a modeling framework for systems with a large number of interacting agents. They have applications in economics, finance, and game theory. Normalizing flows (NFs) are a family of deep generative models that…

Optimization and Control · Mathematics 2023-05-24 Han Huang , Jiajia Yu , Jie Chen , Rongjie Lai

This paper studies mean-field control with joint law dependence under dynamic expectation constraints and/or dynamic state-control-law constraints. We pioneer the establishment of the stochastic maximum principle (SMP) and the derivation of…

Optimization and Control · Mathematics 2026-04-24 Lijun Bo , Jingfei Wang , Xiang Yu

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 address in this paper a fundamental question that arises in mean-field games (MFGs), namely whether mean-field equilibria (MFE) for discrete-time finite-horizon MFGs can be used to obtain approximate stationary as well as non-stationary…

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