Related papers: Mean-field selective optimal control via transient…
We consider a mean-field control problem in which admissible controls are required to be adapted to the common noise filtration. The main objective is to show how the mean-field control problem can be approximates by time consistent…
We consider the problem of controlling the group behavior of a large number of dynamic systems that are constantly interacting with each other. These systems are assumed to have identical dynamics (e.g., birds flock, robot swarm) and their…
In this work, we investigate the optimal control problem for continuous-time Markov decision processes with the random impact of the environment. We provide conditions to show the existence of optimal controls under finite-horizon criteria.…
In this work we are interested in the mean-field formulation of kinetic models under control actions where the control is formulated through a model predictive control strategy (MPC) with varying horizon. The relation between the (usually…
In this paper, a stochastic dynamic control strategy is presented to prevent the spread of an infection over a homogeneous network. The infectious process is persistent, i.e., it continues to contaminate the network once it is established.…
This paper considers a mean field game model inspired by crowd motion where agents want to leave a given bounded domain through a part of its boundary in minimal time. Each agent is free to move in any direction, but their maximal speed is…
In this work we are interested in the modelling and control of opinion dynamics spreading on a time evolving network with scale-free asymptotic degree distribution. The mathematical model is formulated as a coupling of an opinion alignment…
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…
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)…
We investigate reinforcement learning in the setting of Markov decision processes for a large number of exchangeable agents interacting in a mean field manner. Applications include, for example, the control of a large number of robots…
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 optimal control problems for systems governed by mean-field stochastic differential equations, where the control enters both the drift and the diffusion coefficient. We study the relaxed model, in which admissible controls are…
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…
In this paper we consider a mean field approach to modeling the agents flow over a transportation network. In particular, beside a standard framework of mean field games, with controlled dynamics by the agents and costs mass-distribution…
We study the convergence problem of mean-field control theory in the presence of state constraints and non-degenerate idiosyncratic noise. Our main result is the convergence of the value functions associated to stochastic control problems…
In the present work we deal with the existence of solutions for optimal control problems associated to transport equations. The behaviour of a population of individuals will be influenced by the presence of a population of control agents…
Interacting particle systems are known for their ability to generate large-scale self-organized structures from simple local interaction rules between each agent and its neighbors. In addition to studying their emergent behavior, a main…
In this paper we prove a necessary condition of the optimal control problem for a class of general mean-field forward-backward stochastic systems with jumps in the case where the diffusion coefficients depend on control, the control set…
We study a high-dimensional stochastic optimization problem which features both control and stopping. In particular, a central planner steers a large population of particles, and can also remove particles at any time by paying a penalty. In…
Independent sample generation is the prevailing paradigm in modern diffusion-based generative models of AI. We ask a different question: can samples \emph{coordinate} through shared population statistics to transport probability mass more…