相关论文: Mean-field limit for a class of stochastic ergodic…
In ergodic singular stochastic control problems, a decision-maker can instantaneously adjust the evolution of a state variable using a control of bounded variation, with the goal of minimizing a long-term average cost functional. The cost…
This paper outlines a novel extension of the classical Pontryagin minimum (maximum) principle to stochastic optimal control problems. Contrary to the well-known stochastic Pontryagin minimum principle involving forward-backward stochastic…
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…
We derive a framework to compute optimal controls for problems with states in the space of probability measures. Since many optimal control problems constrained by a system of ordinary differential equations (ODE) modelling interacting…
We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model by an $N$-particle…
We investigated a cost-constrained static ergodic control problem of the variance of measure-valued affine processes and its application in streamflow management. The controlled system is a jump-driven mixed moving average process that…
We investigate the global numerical approximation of a class of extended mean field control problems (MFC), where the dynamics and costs depend on the joint distribution of the state and the control. We propose a framework to approximate…
We study the optimal control of general stochastic McKean-Vlasov equation. Such problem is motivated originally from the asymptotic formulation of cooperative equilibrium for a large population of particles (players) in mean-field…
We establish existence of Markov chains of mean-field type with unbounded jump intensities by means of a fixed point argument using the Total Variation distance. We further show existence of nearly-optimal controls and, using a Markov chain…
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…
After proving existence and uniqueness of ergodic distribution dependent backward stochastic differential equations (BSDEs) under strong and weak dissipativity regimes for the underlying McKean--Vlasov SDE, we leverage this new framework to…
We study a stochastic optimal control problem motivated by the operation of a large ensemble of residential storage devices coordinated by an energy aggregator. The aggregator remunerates prosumers in exchange for direct control of their…
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 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…
In this paper we are interested in a new type of {\it mean-field}, non-Markovian stochastic control problems with partial observations. More precisely, we assume that the coefficients of the controlled dynamics depend not only on the paths…
We consider a generic, suitable class of optimal control problems under a constraint given by a finite-dimensional SDE-ODE system, describing a system of two interacting species of particles: the herd, described by SDEs, and the herders,…
This paper is concerned with a mean-field linear quadratic (LQ, for short) optimal control problem with deterministic coefficients. It is shown that convexity of the cost functional is necessary for the finiteness of the mean-field LQ…
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…
The goal of this work is to obtain optimal rates for the convergence problem in mean field control. Our analysis covers cases where the solutions to the limiting problem may not be unique nor stable. Equivalently the value function of the…
Motivated by continuous-time optimal inventory management, we study a class of stationary mean-field control problems with singular controls. The dynamics are modeled by a mean-reverting Ornstein-Uhlenbeck process, and the performance…