  We derive a recursion relation for loop-level scattering amplitudes of
Lagrangian field theories that generalises the tree-level Berends-Giele
recursion relation in Yang-Mills theory. The origin of this recursion relation
is the homological perturbation lemma, which allows us to compute scattering
amplitudes from minimal models of quantum homotopy algebras in a recursive way.
As an application of our techniques, we give an alternative proof of the
relation between non-planar and planar colour-stripped scattering amplitudes.
