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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 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…

Optimization and Control · Mathematics 2025-11-07 Mao Fabrice Djete

We consider extended mean-field control problems with multi-dimensional singular controls. A key challenge when analysing singular controls are jump costs. When controls are one-dimensional, jump costs are most naturally computed by linear…

Mathematical Finance · Quantitative Finance 2025-09-16 Robert Denkert , Ulrich Horst

In this paper, we study the maximum principle of mean field type control problems when the volatility function depends on the state and its measure and also the control, by using our recently developed method. Our method is to embed the…

Optimization and Control · Mathematics 2023-09-14 Alain Bensoussan , Ziyu Huang , Sheung Chi Phillip Yam

In this work, we investigate a stochastic control framework for global optimization over both Euclidean spaces and the Wasserstein space of probability measures, where the objective function may be non-convex and/or non-differentiable. In…

Optimization and Control · Mathematics 2026-04-21 Jinniao Qiu

This paper studies a class of time-inconsistent mean field control (MFC) problems in the presence of common noise under non-exponential discount and joint law dependence of both state and control. We investigate the closed-loop…

Optimization and Control · Mathematics 2025-05-06 Zongxia Liang , Xiang Yu , Keyu Zhang

This paper studies the $N$-particle systems as well as the HJB/master equations for a class of generalized mean field control (MFC) problems and the corresponding potential mean field games of control (MFGC). A local in time classical…

Optimization and Control · Mathematics 2025-04-15 Huafu Liao , Chenchen Mou

The paper focuses on mean-field type multi-agent control problems with finite state and action spaces where the dynamics and cost structures are symmetric and homogeneous, and are affected by the distribution of the agents. A standard…

Optimization and Control · Mathematics 2025-07-03 Erhan Bayraktar , Ali D. Kara

We establish the convergence of the deep actor-critic reinforcement learning algorithm presented in [Angiuli et al., 2023a] in the setting of continuous state and action spaces with an infinite discrete-time horizon. This algorithm provides…

Optimization and Control · Mathematics 2025-11-11 Jean-Pierre Fouque , Mathieu Laurière , Mengrui Zhang

We consider a deterministic mean field games problem in which a typical agent solves an optimal control problem where the dynamics is affine with respect to the control and the cost functional has a growth which is polynomial with respect…

Optimization and Control · Mathematics 2023-05-03 Justina Gianatti , Francisco J. Silva , Ahmad Zorkot

The goal of this work is to obtain optimal rates for the convergence problem in mean field control. Our analysis covers cases where the solutions to the limiting problem may not be unique nor stable. Equivalently the value function of the…

Optimization and Control · Mathematics 2023-05-16 Samuel Daudin , François Delarue , Joe Jackson

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

Finite-state mean-field games (MFGs) arise as limits of large interacting particle systems and are governed by an MFG system, a coupled forward-backward differential equation consisting of a forward Kolmogorov-Fokker-Planck (KFP) equation…

Optimization and Control · Mathematics 2026-02-16 William Hofgard , Asaf Cohen , Mathieu Laurière

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…

Numerical Analysis · Mathematics 2022-01-11 Haoya Li , Yuwei Fan , Lexing Ying

In the presence of a common noise, we study the convergence problems in mean field game (MFG) and mean field control (MFC) problem where the cost function and the state dynamics depend upon the joint conditional distribution of the…

Probability · Mathematics 2023-08-29 Mao Fabrice Djete

In this paper, we extend a recently introduced multi-fidelity control variate for the uncertainty quantification of the Boltzmann equation to the case of kinetic models arising in the study of multiagent systems. For these phenomena, where…

Numerical Analysis · Mathematics 2021-02-05 Lorenzo Pareschi , Torsten Trimborn , Mattia Zanella

This work puts forward a novel numerical approach for solving the stochastic optimal control problem (SOCP) and the mean field control (MFC) problem using projection algorithm inspired by the stochastic maximum principle (SMP) which is also…

Optimization and Control · Mathematics 2026-04-09 Hui Sun

This paper considers a linear-quadratic (LQ) mean field control problem involving a major player and a large number of minor players, where the dynamics and costs depend on random parameters. The objective is to optimize a social cost as a…

Optimization and Control · Mathematics 2019-04-09 Minyi Huang , Son Luu Nguyen

In the paper, we use the equivalent formulation of a finite state mean field game as a control problem with mixed constraints to study the dependence of solutions to finite state mean field game on an initial distribution of players. We…

Optimization and Control · Mathematics 2021-09-16 Yurii Averboukh

In a mean field game of controls, a large population of identical players seek to minimize a cost that depends on the joint distribution of the states of the players and their controls. We first consider the classes of mean field games of…

Optimization and Control · Mathematics 2025-12-05 P. Jameson Graber , Kyle Rosengartner