Related papers: Mean-field selective optimal control via transient…
This paper focuses on the role of a government of a large population of interacting agents as a mean field optimal control problem derived from deterministic finite agent dynamics. The control problems are constrained by a PDE of…
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…
The mean-field analysis of a multi-population agent-based model is performed. The model couples a particle dynamics driven by a nonlocal velocity with a Markow-type jump process on the probability that each agent has of belonging to a given…
We introduce the concept of {\it mean-field optimal control} which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional…
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…
Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game…
We consider mean-field control problems in discrete time with discounted reward, infinite time horizon and compact state and action space. The existence of optimal policies is shown and the limiting mean-field problem is derived when the…
We study a multi-agent mean field type control problem in discrete time where the agents aim to find a socially optimal strategy and where the state and action spaces for the agents are assumed to be continuous. The agents are only weakly…
This paper focuses on a model for opinion dynamics, where the influence weights of agents evolve in time. We formulate a control problem of consensus type, in which the objective is to drive all agents to a final target point under suitable…
In this paper we model the role of a government of a large population as a mean field optimal control problem. Such control problems are constrainted by a PDE of continuity-type, governing the dynamics of the probability distribution of the…
We study a multiscale approach for the control of agent-based, two-population models. The control variable acts over one population of leaders, which influence the population of followers via the coupling generated by their interaction. We…
This paper investigates the social optimality of linear quadratic mean field control systems with unmodeled dynamics. The objective of agents is to optimize the social cost, which is the sum of costs of all agents. By variational analysis…
This paper analyzes and explicitly solves a class of long-term average impulse control problems with a specific mean-field interaction. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The…
In this paper we consider a mean field optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a…
Multi-agent reinforcement learning methods have shown remarkable potential in solving complex multi-agent problems but mostly lack theoretical guarantees. Recently, mean field control and mean field games have been established as a…
In this paper the optimal control of alignment models composed by a large number of agents is investigated in presence of a selective action of a controller, acting in order to enhance consensus. Two types of selective controls have been…
Controlling large particle systems in collective dynamics by a few agents is a subject of high practical importance, e.g., in evacuation dynamics. In this paper we study an instantaneous control approach to steer an interacting particle…
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…
The stochastic optimal control of many agents is an important problem in various fields. We investigate the problem of partial observations, where the state of each agent is not fully observed and the control must be decided based on noisy…
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…