Propagation of chaos for mean-field planning and Schrödinger optimal control problems

We study the propagation of chaos phenomenon for controlled systems of N particles whose dynamics solving Markovian optimal control problems. In the large-N limit, these systems are expected to converge to deterministic optimal control problems of McKeanVlasov (mean-field) type. We focus on the cases where the limit problem is a mean-field planning problem or a mean-field Schrödinger problem, which generalize classical optimal transport by prescribing both the initial and terminal distributions. The proof combines compactness arguments for flows of probability measures in Wasserstein spaces with a generalized de Finetti theorem adapted to the associated transport equation. This talk is based on joint work with Chiara Rigoni.