  In this paper we propose a reduction scheme for polydifferential operators
phrased in terms of $L_\infty$-morphisms. The desired reduction
$L_\infty$-morphism has been obtained by applying an explicit version of the
homotopy transfer theorem. Finally, we prove that the reduced star product
induced by this reduction $L_\infty$-morphism and the reduced star product
obtained via the formal Koszul complex are equivalent.
