Stochastic McKean-Vlasov control problems: a description based on optimal transport

Rigoni Chiara, University of Vienna
De Vecchi Francesco, University of Pavia

We study the convergence of an N-particle Markovian controlled system to the solution of some (finite horizon or Schrödinger-type) stochastic McKean-Vlasov control problem. In particular, under suitable assumptions, we prove the convergence of the value functions, of the fixed time probability laws and of the relative entropy in their path space measures. These proofs are based on a Benamou-Brenier type reformulation of the problem and on the superposition principle, both these tools coming from the theory of optimal transport.

Area: CS33 - Measures, optimal transport and quantum systems (Francesco De Vecchi)

Keywords: McKean-Vlasov optimal control, convergence problem, optimal transport theory, Schrödinger problem

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