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This paper proposes a multiscale method for solving the numerical solution of mean field games which accelerates the convergence and addresses the problem of determining the initial guess. Starting from an approximate solution at the…

This paper presents a Gaussian Process (GP) framework, a non-parametric technique widely acknowledged for regression and classification tasks, to address inverse problems in mean field games (MFGs). By leveraging GPs, we aim to recover…

Here, we consider one-dimensional forward-forward mean-field games (MFGs) with congestion, which were introduced to approximate stationary MFGs. We use methods from the theory of conservation laws to examine the qualitative properties of…

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…

We investigate mean-field games (MFG) in which agents can actively control their speed of access to information. Specifically, the agents can dynamically decide to obtain observations with reduced delay by accepting higher observation…

In the present work, we study deterministic mean field games (MFGs) with finite time horizon in which the dynamics of a generic agent is controlled by the acceleration. They are described by a system of PDEs coupling a continuity equation…

We propose a novel mean field games (MFGs) based GAN(generative adversarial network) framework. To be specific, we utilize the Hopf formula in density space to rewrite MFGs as a primal-dual problem so that we are able to train the model via…

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…

We propose two numerical methods for the optimal control of McKean-Vlasov dynamics in finite time horizon. Both methods are based on the introduction of a suitable loss function defined over the parameters of a neural network. This allows…

Multiagent reinforcement learning algorithms have not been widely adopted in large scale environments with many agents as they often scale poorly with the number of agents. Using mean field theory to aggregate agents has been proposed as a…

The mean field games (MFG) paradigm was introduced to provide tractable approximations of games involving very large populations. The theory typically rests on two key assumptions: homogeneity, meaning that all players share the same…

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…

Mean-field games arise in various fields including economics, engineering, and machine learning. They study strategic decision making in large populations where the individuals interact via certain mean-field quantities. The ground metrics…

In this paper, we investigate a class of Mean Field Games (MFGs) in which the state dynamics are governed by multidimensional reflected stochastic differential equations (SDEs). We establish the existence of an equilibrium and show that it…

An iterative finite difference scheme for mean field games (MFGs) is proposed. The target MFGs are derived from control problems for multidimensional systems with advection terms. For such MFGs, linearization using the Cole-Hopf…

We consider discrete-time stationary mean field games (MFG) with unknown dynamics and design algorithms for finding the equilibrium with finite-time complexity guarantees. Prior solutions to the problem assume either the contraction of a…

This paper presents a general mean-field game (GMFG) framework for simultaneous learning and decision-making in stochastic games with a large population. It first establishes the existence of a unique Nash Equilibrium to this GMFG, and…

This paper introduces and analyzes a new class of mean-field control (\textsc{MFC}) problems in which agents interact through a \emph{fixed but controllable} network structure. In contrast with the classical \textsc{MFC} framework -- where…

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…

The policy iteration method is a classical algorithm for solving optimal control problems. In this paper, we introduce a policy iteration method for Mean Field Games systems, and we study the convergence of this procedure to a solution of…