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In this work, we systematically investigate mean field games and mean field type control problems with multiple populations using a coupled system of forward-backward stochastic differential equations of McKean-Vlasov type stemming from…

Probability · Mathematics 2020-11-03 Masaaki Fujii

We consider a data-driven formulation of the classical discrete-time stochastic control problem. Our approach exploits the natural structure of many such problems, in which significant portions of the system are uncontrolled. Employing the…

Optimization and Control · Mathematics 2025-08-25 Boris Baros , Samuel N. Cohen , Christoph Reisinger

We consider interacting agent systems with a large number of stochastic agents (or particles) influenced by a fixed number of external stochastic lead agents. Such examples arise, for example in models of opinion dynamics, where a small…

Optimization and Control · Mathematics 2025-12-23 Sebastian Zimper , Ana Djurdjevac , Carsten Hartmann , Christof Schütte , Nataša Djurdjevac Conrad

Multi-agent reinforcement learning (MARL), despite its popularity and empirical success, suffers from the curse of dimensionality. This paper builds the mathematical framework to approximate cooperative MARL by a mean-field control (MFC)…

Machine Learning · Computer Science 2021-10-04 Haotian Gu , Xin Guo , Xiaoli Wei , Renyuan Xu

Modeling heterogeneous and multi-lane traffic flow is essential for understanding and controlling complex transportation systems. In this work, we consider three vehicle populations: two classes of human-driven vehicles (cars and trucks)…

Optimization and Control · Mathematics 2025-10-17 Maria Teresa Chiri , Christopher Denaro , Xiaoqian Gong , Benedetto Piccoli

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

Learning how to learn efficiently is a fundamental challenge for biological agents and a growing concern for artificial ones. To learn effectively, an agent must regulate its learning speed, balancing the benefits of rapid improvement…

Machine Learning · Computer Science 2026-01-13 Valentina Njaradi , Rodrigo Carrasco-Davis , Peter E. Latham , Andrew Saxe

Methods like multi-agent reinforcement learning struggle to scale with growing population size. Mean-field games (MFGs) are a game-theoretic approach that can circumvent this by finding a solution for an abstract infinite population, which…

Multiagent Systems · Computer Science 2025-12-23 Patrick Benjamin , Alessandro Abate

We present a Reinforcement Learning (RL) algorithm to solve infinite horizon asymptotic Mean Field Game (MFG) and Mean Field Control (MFC) problems. Our approach can be described as a unified two-timescale Mean Field Q-learning: The…

Optimization and Control · Mathematics 2021-06-01 Andrea Angiuli , Jean-Pierre Fouque , Mathieu Laurière

We consider a class of mean field games in which the agents interact through both their states and controls, and we focus on situations in which a generic agent tries to adjust her speed (control) to an average speed (the average is made in…

Analysis of PDEs · Mathematics 2020-03-10 Y Achdou , Z Kobeissi

The processes of interplant competition within a field are still poorly understood. However, they explain a large part of the heterogeneity in a field and may have longer-term consequences, especially in mixed stands. Modeling can help to…

Analysis of PDEs · Mathematics 2019-06-05 Antonin Della Noce , Amélie Mathieu , Paul-Henry Cournède

Mean Field Games (MFGs) provide a powerful framework for modeling the collective behavior of large populations of interacting agents. In this paper, we address the problem of Imitation Learning (IL) in MFGs subject to common noise, where…

Machine Learning · Computer Science 2026-05-06 Grégoire Lambrecht , Mathieu Laurière

We study high-dimensional stochastic optimal control problems in which many agents cooperate to minimize a convex cost functional. We consider both the full-information problem, in which each agent observes the states of all other agents,…

Probability · Mathematics 2023-01-10 Joe Jackson , Daniel Lacker

A learning based method for obtaining feedback laws for nonlinear optimal control problems is proposed. The learning problem is posed such that the open loop value function is its optimal solution. This infinite dimensional, function space,…

Optimization and Control · Mathematics 2022-10-26 Karl Kunisch , Donato Vásquez-Varas , Daniel Walter

The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering…

Probability · Mathematics 2017-05-11 Mahmoud Talebi , Jan Friso Groote , Jean-Paul Linnartz

Machine learning (ML) methods are highly flexible, but their ability to approximate the true data-generating process is fundamentally constrained by finite samples. We characterize a universal lower bound, the Limits-to-Learning Gap (LLG),…

Machine Learning · Statistics 2025-12-16 Zhimin Chen , Bryan Kelly , Semyon Malamud

A self-learning approach for optimal feedback gains for finite-horizon nonlinear continuous time control systems is proposed and analysed. It relies on parameter dependent approximations to the optimal value function obtained from a family…

Optimization and Control · Mathematics 2023-02-28 Karl Kunisch , Daniel Walter

We introduce the rigorous limit process connecting finite dimensional sparse optimal control problems with ODE constraints, modeling parsimonious interventions on the dynamics of a moving population divided into leaders and followers, to an…

Optimization and Control · Mathematics 2015-06-18 Massimo Fornasier , Benedetto Piccoli , Francesco Rossi

In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…

Optimization and Control · Mathematics 2024-06-18 Gokce Dayanikli , Mathieu Lauriere

Subject to reasonable conditions, in large population stochastic dynamics games, where the agents are coupled by the system's mean field (i.e. the state distribution of the generic agent) through their nonlinear dynamics and their nonlinear…

Optimization and Control · Mathematics 2019-05-28 Nevroz Sen , Peter E. Caines