General Presentation of Mean Field Control Problems

2013 ◽  
pp. 7-9
Author(s):  
Alain Bensoussan ◽  
Jens Frehse ◽  
Phillip Yam
Keyword(s):  
Mean Field ◽  
Control Problems ◽  
Field Control

scholarly journals Finite state N-agent and mean field control problems

2021 ◽  
Author(s):  
Alekos Cecchin
Keyword(s):  
Control Problem ◽  
Value Function ◽  
Mean Field ◽  
Control Problems ◽  
Value Functions ◽  
Limit Value ◽  
Field Control ◽  
Finite State ◽  
Finite Time Horizon ◽  
Hamilton Jacobi Bellman

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 Hamilton-Jacobi-Bellman equation in the simplex. In absence of any convexity assumption, we exploit this characterization to prove convergence, as $N$ grows, of the value functions of the centralized $N$-agent optimal control problem to the limit mean field control problem  value function, with a convergence rate of order $\frac{1}{\sqrt{N}}$. Then, assuming convexity, we show that the limit value function is smooth and establish propagation of chaos, i.e.  convergence of the $N$-agent optimal trajectories to the unique limiting optimal trajectory, with an explicit rate.

scholarly journals Extended Mean Field Control Problems: Stochastic Maximum Principle and Transport Perspective

2019 ◽  
Vol 57 (6) ◽  
pp. 3666-3693 ◽  
Author(s):  
Beatrice Acciaio ◽  
Julio Backhoff-Veraguas ◽  
René Carmona
Keyword(s):  
Maximum Principle ◽  
Mean Field ◽  
Stochastic Maximum Principle ◽  
Control Problems ◽  
Field Control

scholarly journals Generalized dynamic programming principle and sparse mean-field control problems

2020 ◽  
Vol 481 (1) ◽  
pp. 123437 ◽  
Author(s):  
Giulia Cavagnari ◽  
Antonio Marigonda ◽  
Benedetto Piccoli
Keyword(s):  
Dynamic Programming ◽  
Mean Field ◽  
Dynamic Programming Principle ◽  
Control Problems ◽  
Field Control

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

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