  We study the low energy effective action $S$ of gravity, induced by
integrating out gauge and matter fields, in a general class of Randall-Sundrum
type string compactification scenarios with exponential warp factors. Our
method combines dimensional reduction with the holographic map between between
5-d supergravity and 4-d large $N$ field theory. Using the classical
supergravity approximation, we derive a flow equation of the effective action
$S$ that controls its behavior under scale transformations. We find that as a
result each extremum of $S$ automatically describes a complete RG trajectory of
classical solutions. This implies that, provided the cosmological constant is
canceled in the high energy theory, classical flat space backgrounds naturally
remain stable under the RG-flow. The mechanism responsible for this stability
is that the non-zero vacuum energy generated by possible phase transitions, is
absorbed by a dynamical adjustment of the contraction rate of the warp factor.
