  A `novel' pure theory of Einstein-Gauss-Bonnet gravity in four-spacetime
dimensions can be constructed by rescaling the Gauss-Bonnet coupling constant,
seemingly eluding Lovelock's theorem. Recently, however, the well-posedness of
this model has been called into question. Here we apply a `dimensional
regularization' technique, first used by Mann and Ross to write down a $D\to2$
limit of general relativity, to the case of pure Einstein-Gauss-Bonnet gravity.
The resulting four-dimensional action is a particular Horndeski theory of
gravity matching the result found via a Kaluza-Klein reduction over a flat
internal space. Some cosmological solutions of this four-dimensional theory are
examined. We further adapt the technique to higher curvature Lovelock theories
of gravity, as well as a low-energy effective string action with an $\alpha'$
correction. With respect to the $D\to4$ limit of the $\alpha'$-corrected string
action, we find we must also rescale the dilaton to have a non-singular action
in four dimensions. Interestingly, when the conformal rescaling $\Phi$ is
interpreted as another dilaton, the regularized string action appears to be a
special case of a covariant multi-Galileon theory of gravity.
