  We performed a functional renormalization group analysis for the quantum
Einstein gravity including a quadratic term in the curvature. The ultraviolet
non-gaussian fixed point and its critical exponent for the correlation length
are identified for different forms of regulators in case of dimension 3. We
searched for that optimized regulator where the physical quantities show the
least regulator parameter dependence. It is shown that the Litim regulator
satisfies this condition. The infrared fixed point has also been investigated,
it is found that the exponent is insensitive to the third coupling introduced
by the $R^2$ term.
