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Finite state N-agent and mean field control problems

Abstract : 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  . 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.
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Contributor : Edp Sciences <>
Submitted on : Wednesday, April 7, 2021 - 10:15:41 PM
Last modification on : Friday, April 9, 2021 - 3:32:12 AM


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Alekos Cecchin. Finite state N-agent and mean field control problems. ESAIM: Control, Optimisation and Calculus of Variations, EDP Sciences, 2021, 27, pp.31. ⟨10.1051/cocv/2021032⟩. ⟨hal-03192295⟩