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Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2021

Finite state N-agent and mean field control problems

Résumé

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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Dates et versions

hal-03192295 , version 1 (07-04-2021)

Identifiants

Citer

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