Similarly to the idea of Wilson efective action where some degrees of freedom are integrated out, in BV-formalism one introduces BV-effective action; using a variant of integration utilizing Lagrangean submanifolds. In this procedure BV integrals are involved.
This is related to solving quantum master equation where the “induction” data are equivalent to the data involved in homological perturbation theory.
Albert Schwarz, Geometry of BV quantization, CMP 1993
Losev
Cattaneo, Felder 2008