  We initiate the continuum description of a non-perturbative 5d lattice
Yang-Mills model with 4d boundaries using the $\varepsilon$-expansion. In its
simplest version classically the bulk has an $SU(2)$ gauge symmetry and on the
boundary there is an Abelian-Higgs system with zero scalar potential. In part I
we compute the Renormalization Group flows and related quantities in a limit
where the boundary decouples from the bulk.
