相关论文: Mean-Field Sparse Optimal Control

We present a linear--quadratic Stackelberg game with a large number of followers and we also derive the mean field limit of infinitely many followers. The relation between optimization and mean-field limit is studied and conditions for…

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…

In many multi-agent systems of practical interest, such as traffic networks or crowd evacuation, control actions cannot be exerted on all agents. Instead, controllable leaders must indirectly steer uncontrolled followers through local…

Mean field limits are an important tool in the context of large-scale dynamical systems, in particular, when studying multiagent and interacting particle systems. While the continuous-time theory is well-developed, few works have considered…

We discuss and compare two methods of investigations for the asymptotic regime of stochastic differential games with a finite number of players as the number of players tends to the infinity. These two methods differ in the order in which…

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 rigorously connects the problem of optimal control of McKean-Vlasov dynamics with large systems of interacting controlled state processes. Precisely, the empirical distributions of near-optimal control-state pairs for the…

Recent work linking deep neural networks and dynamical systems opened up new avenues to analyze deep learning. In particular, it is observed that new insights can be obtained by recasting deep learning as an optimal control problem on…

We consider particle-based stochastic reaction-drift-diffusion models where particles move via diffusion and drift induced by one- and two-body potential interactions. The dynamics of the particles are formulated as measure-valued…

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…

We study a specific class of finite-horizon mean field optimal stopping problems by means of the dynamic programming approach. In particular, we consider problems where the state process is not affected by the stopping time. Such problems…

We study a family of optimal control problems in which one aims at minimizing a cost that mixes a quadratic control penalization and the variance of the system, both for finitely many agents and for the mean-field dynamics as their number…

In this paper, we investigate the interaction of two populations with a large number of indistinguishable agents. The problem consists in two levels: the interaction between agents of a same population, and the interaction between the two…

In this paper, we first give the existence and uniqueness theorems for generalized mean-filed delay stochastic differential equations (GMFDSDEs) and mean-field anticipated backward stochastic differential equations (MFABSDEs). Then we study…

In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is…

In this work, we study the mean field Schr\"odinger problem from a purely probabilistic point of view by exploiting its connection to stochastic control theory for McKean-Vlasov diffusions. Our main result shows that the mean field…

The focus of this paper is directed towards optimal control of multi-agent systems consisting of one leader and a number of followers in the presence of noise. The dynamics of every agent is assumed to be linear, and the performance index…

In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in…

We study a coupled system of controlled stochastic differential equations (SDEs) driven by a Brownian motion and a compensated Poisson random measure, consisting of a forward SDE in the unknown process $X(t)$ and a \emph{predictive…

Historically, traffic modelling approaches have taken either a particle-like (microscopic) approach, or a gas-like (meso- or macroscopic) approach. Until recently with the introduction of mean-field games to the controls community, there…