  In this paper we study optimal stopping problems for nonlinear Markov
processes driven by a McKean-Vlasov SDE and aim at solving them numerically by
Monte Carlo. To this end we propose a novel regression algorithm based on the
corresponding particle system and prove its convergence. The proof of
convergence is based on perturbation analysis of a related linear regression
problem. The performance of the proposed algorithms is illustrated by a
numerical example.
