  In this report, we discuss a candidate mechanism through which one might
address the various cosmological constant problems. We first observe that the
renormalization of gravitational couplings (induced by integrating out various
matter fields) manifests non-local modifications to Einstein's equations as
quantum corrected equations of motion. That is, at the loop level, matter
sources curvature through a gravitational coupling that is a non-local function
of the covariant d'Alembertian. If the functional form of the resulting
Newton's `constant' is such that it annihilates very long wavelength sources,
but reduces to $1/M^2_{pl}$ ($M_{pl}$ being the 4d Planck mass) for all sources
with cosmologically observable wavelengths, we would have a complimentary
realization of the degravitation paradigm-- a realization through which its
non-linear completion and the corresponding modified Bianchi identities are
readily understood. We proceed to consider various theories whose coupling to
gravity may a priori induce non-trivial renormalizations of Newton's constant
in the IR, and arrive at a class of non-local effective actions which yield a
suitably degravitating filter function for Newton's constant upon subsequently
being integrated out. We motivate this class of non-local theories through
several considerations, discuss open issues, future directions, the inevitable
question of scheme dependence in semi-classical gravitational calculations and
comment on connections with other meditations in the literature on relaxing of
the cosmological constant semi-classically.
