  In this paper, inspired by the Costello's seminal work, we present a general
formulation of exact renormalization group (RG) within the Batalin-Vilkovisky
(BV) quantization scheme. In the spirit of effective field theory, the BV
bracket and Laplacian structure as well as the BV effective action (EA) depend
on an effective energy scale. The BV EA at a certain scale satisfies the BV
quantum master equation at that scale. The RG flow of the EA is implemented by
BV canonical maps intertwining the BV structures at different scales.
Infinitesimally, this generates the BV exact renormalization group equation
(RGE). We show that BV RG theory can be extended by augmenting the scale
parameter space R to its shifted tangent bundle T[1]R. The extra odd direction
in scale space allows for a BV RG supersymmetry that constrains the structure
of the BV RGE bringing it to Polchinski's form. We investigate the implications
of BV RG supersymmetry in perturbation theory. Finally, we illustrate our
findings by constructing free models of BV RG flow and EA exhibiting RG
supersymmetry in the degree -1 symplectic framework and studying the
perturbation theory thereof. We find in particular that the odd partner of
effective action describes perturbatively the deviation of the interacting RG
flow from its free counterpart.
