  We reformulate the recently proposed regularized version of Lovelock gravity
in four dimensions as a scalar-tensor theory. By promoting the warp factor of
the internal space to a scalar degree of freedom by means of Kaluza-Klein
reduction, we show that regularized Lovelock gravity can be described
effectively by a certain subclass of the Horndeski theory. Cosmological aspects
of this particular scalar-tensor theory are studied. It is found that the
background with a scalar charge is generically allowed. The consequences of
this scalar charge are briefly discussed.
