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• W3093518555 abstract "We examine mean field control problems (MFCP) on a finite state space, in continuous time and over a finite time horizon. We characterize the value function of the MFCP as the unique viscosity solution of a HJB 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 MFCP value function, with a convergence rate of order $1/sqrt{N}$. Then, assuming convexity, we show that the limit HJB admits a smooth solution and establish propagation of chaos, i.e. convergence of the $N$-agent optimal trajectory to the unique limiting optimal trajectory, with an explicit rate." @default.
• W3093518555 created "2020-10-29" @default.
• W3093518555 creator A5066278454 @default.
• W3093518555 date "2020-10-22" @default.
• W3093518555 modified "2023-09-27" @default.
• W3093518555 title "Finite state N-agent and mean field control problems" @default.
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• W3093518555 hasPublicationYear "2020" @default.
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