  Working in scalar field theory, we consider RG trajectories which correspond
to nonrenormalizable theories, in the Wilsonian sense. An interesting question
to ask of such trajectories is, given some fixed starting point in parameter
space, how the effective action at the effective scale, Lambda, changes as the
bare scale (and hence the duration of the flow down to Lambda) is changed. When
the effective action satisfies Polchinski's version of the Exact
Renormalization Group equation, we prove, directly from the path integral, that
the dependence of the effective action on the bare scale, keeping the
interaction part of the bare action fixed, is given by an equation of the same
form as the Polchinski equation but with a kernel of the opposite sign. We then
investigate whether similar equations exist for various generalizations of the
Polchinski equation. Using nonperturbative, diagrammatic arguments we find that
an action can always be constructed which satisfies the Polchinski-like
equation under variation of the bare scale. For the family of flow equations in
which the field is renormalized, but the blocking functional is the simplest
allowed, this action is essentially identified with the effective action at
Lambda = 0. This does not seem to hold for more elaborate generalizations.
