  We consider SU(2) Yang-Mills theory on $AdS_4$ by imposing various boundary
conditions, which correspond to non-trivial deformations of its boundary $CFT$.
We obtain classical solutions of Yang-Mills fields up to the first subleading
order correction by using small amplitude expansion of the gauge field without
considering gravitational back reaction. We also consider SU(2) Yang-Mills
instanton solution in $AdS_4$ bulk, and propose a boundary action. It turns out
that the boundary theory is the Chern Simons theory with a non-local
deformation which has the form similar to the Wilson line. In the limit of the
deformation parameter $\rho \rightarrow \infty$, this non-local deformation is
suppressed and the boundary theory becomes pure Chern Simons. For large but
finite values of $\rho$, this non-local deformation can be treated
perturbatively within the Chern-Simon theory.
