Related papers: Extended mean field control problem: a propagation…
This paper studies a stochastic mean-field linear-quadratic optimal control problem with random coefficients. The state equation is a general linear stochastic differential equation with mean-field terms $\EE X(t)$ and $\EE u(t)$ of the…
We provide a new version of the Tikhonov theorem for both two-scale forward systems and also two-scale forward-backward systems of stochastic differential equations, which also covers the McKean-Vlasov case. Differently from what is usually…
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…
Mean field control (MFC) problems have been introduced to study social optima in very large populations of strategic agents. The main idea is to consider an infinite population and to simplify the analysis by using a mean field…
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…
We discuss the system of Fokker-Planck and Hamilton-Jacobi-Bellman equations arising from the finite horizon control of McKean-Vlasov dynamics. We give examples of existence and uniqueness results. Finally, we propose some simple models for…
This paper studies optimal control and stabilization problems for continuous-time mean-field systems with input delay, which are the fundamental development of control and stabilization problems for mean-field systems. There are two main…
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…
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…
We study a class of mean-field control problems under partial observation. The controlled dynamics are of McKean-Vlasov type and are subject to regime switching driven by a hidden Markov chain. The observation process depends on the control…
Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to…
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 examine mean field control problems on a finite state space, in continuous time and over a finite time horizon. We characterize the value function of the mean field control problem as the unique viscosity solution of a…
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…
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…
We derive the mean-field equations arising as the limit of a network of interacting spiking neurons, as the number of neurons goes to infinity. The neurons belong to a fixed number of populations and are represented either by the…
We study the optimal control problem for a weighted mean-field system. A new feature of the control problem is that the coefficients depend on the state process as well as its weighted measure and the control variable. By applying…
We study a mean field optimal control problem with general non-Markovian dynamics, including both common noise and jumps. We show that its minimizers are Nash equilibria of an associated mean field game of controls. These types of games are…
We study the asymptotics of the point process induced by an interacting particle system with mean-field drift interaction. Under suitable assumptions, we establish propagation of chaos for this point process: it has the same weak limit as…
We analyze a problem of optimal control of the Fokker-Planck equation with state constraints in the Wasserstein space of probability measures. Our main result is to derive optimality conditions in the form of a Mean Field Game system of…