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This paper introduces a framework of Constrained Mean-Field Games (CMFGs), where each agent solves a constrained Markov decision process (CMDP). This formulation captures scenarios in which agents' strategies are subject to feasibility,…

Optimization and Control · Mathematics 2025-10-15 Anran Hu , Zijiu Lyu

In the Bayesian reinforcement learning (RL) setting, a prior distribution over the unknown problem parameters -- the rewards and transitions -- is assumed, and a policy that optimizes the (posterior) expected return is sought. A common…

Machine Learning · Computer Science 2021-09-27 Aviv Tamar , Daniel Soudry , Ev Zisselman

Policy-based reinforcement learning methods suffer from the policy collapse problem. We find valued-based reinforcement learning methods with {\epsilon}-greedy mechanism are capable of enjoying three characteristics, Closed-form Diversity,…

Machine Learning · Computer Science 2021-06-03 Changnan Xiao , Haosen Shi , Jiajun Fan , Shihong Deng

We consider the problem of learning the optimal policy for Markov decision processes with safety constraints. We formulate the problem in a reach-avoid setup. Our goal is to design online reinforcement learning algorithms that ensure safety…

Machine Learning · Computer Science 2026-01-21 Abhijit Mazumdar , Rafal Wisniewski , Manuela L. Bujorianu

We study the error introduced by entropy regularization in infinite-horizon discrete discounted Markov decision processes. We show that this error decreases exponentially in the inverse regularization strength, both in a weighted…

Optimization and Control · Mathematics 2025-12-16 Johannes Müller , Semih Cayci

We consider variational Mean Field Games endowed with a constraint on the maximal density of the distribution of players. Minimizers of the variational formulation are equilibria for a game where both the running cost and the final cost of…

Analysis of PDEs · Mathematics 2019-06-19 Hugo Lavenant , Filippo Santambrogio

Many tasks in modern machine learning can be formulated as finding equilibria in \emph{sequential} games. In particular, two-player zero-sum sequential games, also known as minimax optimization, have received growing interest. It is…

Machine Learning · Computer Science 2019-11-26 Yuanhao Wang , Guodong Zhang , Jimmy Ba

The goal of this paper is to study the long time behavior of solutions of the first-order mean field game (MFG) systems with a control on the acceleration. The main issue for this is the lack of small time controllability of the problem,…

Optimization and Control · Mathematics 2020-07-07 Pierre Cardaliaguet , Cristian Mendico

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

The theory of Mean-Field Games is interested in the behaviour of interacting particle systems in which the individual interaction between particles (players) decreases as the size of the population increases. In recent years, it was…

Optimization and Control · Mathematics 2024-01-23 Daniel Hernández-Hernández , Joshué Helí Ricalde-Guerrero

This paper considers games where the utilities for agents are the sum of a term proportional to a social utility, and another term that is an individual cost or reward. The agents are assumed to be irrational in their perception of the…

Computer Science and Game Theory · Computer Science 2026-05-21 Ashok Krishnan K. S. , Helene Le Cadre , Ana Busic

Mean field games (MFGs) provide a mathematically tractable framework for modelling large-scale multi-agent systems by leveraging mean field theory to simplify interactions among agents. It enables applying inverse reinforcement learning…

Machine Learning · Computer Science 2025-12-02 Yang Chen , Libo Zhang , Jiamou Liu , Michael Witbrock

Mean Field Games (MFGs) offer a powerful framework for studying large-scale multi-agent systems. Yet, learning Nash equilibria in MFGs remains a challenging problem, particularly when the initial distribution is unknown or when the…

Machine Learning · Computer Science 2025-09-04 Zida Wu , Mathieu Lauriere , Matthieu Geist , Olivier Pietquin , Ankur Mehta

We consider N-player and mean field games in continuous time over a finite horizon, where the position of each agent belongs to {-1,1}. If there is uniqueness of mean field game solutions, e.g. under monotonicity assumptions, then the…

Optimization and Control · Mathematics 2019-02-06 Alekos Cecchin , Paolo Dai Pra , Markus Fischer , Guglielmo Pelino

This paper studies a mean field game inspired by crowd motion in which agents evolve in a compact domain and want to reach its boundary minimizing the sum of their travel time and a given boundary cost. Interactions between agents occur…

Optimization and Control · Mathematics 2020-01-31 Samer Dweik , Guilherme Mazanti

We propose a mean field control game model for the intra-and-inter-bank borrowing and lending problem. This framework allows to study the competitive game arising between groups of collaborative banks. The solution is provided in terms of…

Optimization and Control · Mathematics 2022-07-08 Andrea Angiuli , Nils Detering , Jean-Pierre Fouque , Mathieu Laurière , Jimin Lin

This chapter examines monotonicity techniques in the theory of mean-field games(MFGs). Originally, monotonicity ideas were used to establish the uniqueness of solutions for MFGs. Later, monotonicity methods and monotone operators were…

Analysis of PDEs · Mathematics 2025-02-28 Rita Ferreira , Diogo Gomes , Teruo Tada

Designing socially optimal policies in multi-agent environments is a fundamental challenge in both economics and artificial intelligence. This paper studies a general framework for learning Stackelberg equilibria in dynamic and uncertain…

Systems and Control · Electrical Eng. & Systems 2025-09-23 Jun He , Andrew L. Liu , Yihsu Chen

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

The goal of this paper is to show existence of short-time classical solutions to the so called Master Equation of \emph{first order} Mean Field Games, which can be thought of as the limit of the corresponding master equation of a stochastic…

Analysis of PDEs · Mathematics 2019-08-20 Sergio Mayorga