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Related papers: Mean-Field Optimal Control

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This paper investigates the limit behavior of Markov Decision Processes (MDPs) made of independent particles evolving in a common environment, when the number of particles goes to infinity. In the finite horizon case or with a discounted…

Probability · Mathematics 2009-06-10 Nicolas Gast , Bruno Gaujal

In recent years, reinforcement learning and its multi-agent analogue have achieved great success in solving various complex control problems. However, multi-agent reinforcement learning remains challenging both in its theoretical analysis…

Robotics · Computer Science 2023-02-10 Kai Cui , Mengguang Li , Christian Fabian , Heinz Koeppl

We analyze the mean-field limit of a stochastic Schr{\"o}dinger equation arising in quantum optimal control and mean-field games, where N interacting particles undergo continuous indirect measurement. For the open quantum system described…

Analysis of PDEs · Mathematics 2025-07-28 Anne de Bouard , Gaoyue Guo , Théo Hérouard

The optimal control of epidemic-like stochastic processes is important both historically and for emerging applications today, where it can be especially important to include time-varying parameters that impact viral epidemic-like…

Optimization and Control · Mathematics 2017-10-02 Yingdong Lu , Mark S. Squillante , Chai Wah Wu

We develop an exhaustive study of Markov decision process (MDP) under mean field interaction both on states and actions in the presence of common noise, and when optimization is performed over open-loop controls on infinite horizon. Such…

Optimization and Control · Mathematics 2021-09-10 Médéric Motte , Huyên Pham

We consider a finite number of $N$ statistically equal agents, each moving on a finite set of states according to a continuous-time Markov Decision Process (MDP). Transition intensities of the agents and generated rewards depend not only on…

Probability · Mathematics 2025-09-23 Nicole Bäuerle , Sebastian Höfer

Adjustable autonomy refers to entities dynamically varying their own autonomy, transferring decision-making control to other entities (typically agents transferring control to human users) in key situations. Determining whether and when…

Artificial Intelligence · Computer Science 2011-06-24 D. V. Pynadath , P. Scerri , M. Tambe

A dynamic mean field theory is developed for finite state and action Bayesian reinforcement learning in the large state space limit. In an analogy with statistical physics, the Bellman equation is studied as a disordered dynamical system;…

Machine Learning · Statistics 2023-07-13 George Stamatescu

Mean-Field Control (MFC) is a powerful tool to solve Multi-Agent Reinforcement Learning (MARL) problems. Recent studies have shown that MFC can well-approximate MARL when the population size is large and the agents are exchangeable.…

Machine Learning · Computer Science 2022-06-02 Washim Uddin Mondal , Vaneet Aggarwal , Satish V. Ukkusuri

We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that…

Probability · Mathematics 2015-12-01 Huyên Pham , Xiaoli Wei

In this paper we consider mean-field optimal control problems with selective action of the control, where the constraint is a continuity equation involving a non-local term and diffusion. First order optimality conditions are formally…

Optimization and Control · Mathematics 2023-02-02 Giacomo Albi , Marco Caliari , Elisa Calzola , Fabio Cassini

The synthesis of control laws for interacting agent-based dynamics and their mean-field limit is studied. A linearization-based approach is used for the computation of sub-optimal feedback laws obtained from the solution of differential…

Optimization and Control · Mathematics 2021-01-13 G. Albi , M. Herty , D. Kalise , C. Segala

Autonomous systems often have logical constraints arising, for example, from safety, operational, or regulatory requirements. Such constraints can be expressed using temporal logic specifications. The system state is often partially…

Artificial Intelligence · Computer Science 2024-06-21 Krishna C. Kalagarla , Dhruva Kartik , Dongming Shen , Rahul Jain , Ashutosh Nayyar , Pierluigi Nuzzo

Mean field games is a recent area of study introduced by Lions and Lasry in a series of seminal papers in 2006. Mean field games model situations of competition between large number of rational agents that play non-cooperative dynamic games…

Optimization and Control · Mathematics 2011-03-18 Diogo A. Gomes , Joana Mohr , Rafael R. Souza

In this paper, we investigate team optimal control of coupled major-minor subsystems with mean-field sharing. In such a model, there is one major subsystem that directly influences the dynamics of $n$ homogeneous minor subsystems; however,…

Optimization and Control · Mathematics 2020-12-07 Jalal Arabneydi , Aditya Mahajan

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

We establish existence of nearly-optimal controls, conditions for existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean-field type,…

Probability · Mathematics 2017-07-25 Boualem Djehiche , Said Hamadène

Large-scale competitive platforms are interacting multi-agent systems in which latent skills drift over time and pairwise interactions are shaped by matchmaking. We study a controlled rating dynamics in the mean-field limit and derive a…

Optimization and Control · Mathematics 2025-12-29 Wataru Nozawa

We investigate the global numerical approximation of a class of extended mean field control problems (MFC), where the dynamics and costs depend on the joint distribution of the state and the control. We propose a framework to approximate…

Optimization and Control · Mathematics 2026-03-23 Athena Picarelli , Marco Scaratti , Jonathan Tam

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