Related papers: Extended mean field control: a global numerical so…
In this paper, we use mean field games (MFGs) to investigate approximations of $N$-player games with uniformly symmetrically continuous heterogeneous closed-loop actions. To incorporate agents' risk aversion (beyond the classical expected…
These notes present preliminary results regarding two different approximations of linear infinite-horizon optimal control problems arising in model predictive control. Input and state trajectories are parametrized with basis functions and a…
This paper studies social optima and Nash games for mean field linear quadratic control systems, where subsystems are coupled via dynamics and individual costs. For the social control problem, we first obtain a set of forward-backward…
We study optimal control for mean-field forward backward stochastic differential equations with payoff functionals of mean-field type. Sufficient and necessary optimality conditions in terms of a stochastic maximum principle are derived. As…
We study Mean Field stochastic control problems where the cost function and the state dynamics depend upon the joint distribution of the controlled state and the control process. We prove suitable versions of the Pontryagin stochastic…
The mean-field Langevin dynamics (MFLD) minimizes an entropy-regularized nonlinear convex functional on the Wasserstein space over $\mathbb{R}^d$, and has gained attention recently as a model for the gradient descent dynamics of interacting…
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, a risk-aware motion control scheme is considered for mobile robots to avoid randomly moving obstacles when the true probability distribution of uncertainty is unknown. We propose a novel model predictive control (MPC) method…
This paper presents approaches to mean-field control, motivated by distributed control of multi-agent systems. Control solutions are based on a convex optimization problem, whose domain is a convex set of probability mass functions (pmfs).…
This paper analyzes a class of infinite-time-horizon stochastic games with singular controls motivated from the partially reversible problem. It provides an explicit solution for the mean-field game (MFG) and presents sensitivity analysis…
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…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
This paper is mainly concerned with the solutions to both forward and backward mean-field stochastic partial differential equation and the corresponding optimal control problem for mean-field stochastic partial differential equation. We…
This paper investigates the control of a massive population of UAVs such as drones. The straightforward method of control of UAVs by considering the interactions among them to make a flock requires a huge inter-UAV communication which is…
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…
Mean field games are limit models for symmetric $N$-player games with interaction of mean field type as $N\to\infty$. The limit relation is often understood in the sense that a solution of a mean field game allows to construct approximate…
In the present work, we study deterministic mean field games (MFGs) with finite time horizon in which the dynamics of a generic agent is controlled by the acceleration. They are described by a system of PDEs coupling a continuity equation…
Classical neural ordinary differential equations (ODEs) are powerful tools for approximating the log-density functions in high-dimensional spaces along trajectories, where neural networks parameterize the velocity fields. This paper…
We establish an existence of equilibrium result for a class of non-Markovian mean-field games with unbounded control space in weak formulation. Our result is based on new existence and stability results for quadratic-growth generalized…
We consider an optimal control problem with ergodic (long term average) reward for a McKean-Vlasov dynamics, where the coefficients of a controlled stochastic differential equation depend on the marginal law of the solution. Starting from…