  We consider the physics of lattice bosons affected by disordered on-site
interparticle interactions. Characteristic qualitative changes in the zero
temperature phase diagram are observed when compared to the case of randomness
in the chemical potential. The Mott-insulating regions shrink and eventually
vanish for any finite disorder strength beyond a sufficiently large filling
factor. Furthermore, at low values of the chemical potential both the
superfluid and Mott insulator are stable towards formation of a Bose glass
leading to a possibly non-trivial tricritical point. We discuss feasible
experimental realizations of our scenario in the context of ultracold atoms on
optical lattices.
