  Higher derivative theory is one of the important models of quantum gravity,
renormalizable and asymptotically free within the standard perturbative
approach. We consider the $4-\epsilon$ renormalization group for this theory,
an approach which proved fruitful in $2-\epsilon$ models. A consistent
formulation in dimension $n=4-\epsilon$ requires taking quantum effects of the
topological term into account, hence we perform calculation which is more
general than the ones done before. In the special $n=4$ case we confirm a known
result by Fradkin-Tseytlin and Avramidi-Barvinsky, while contributions from
topological term do cancel. In the more general case of $4-\epsilon$
renormalization group equations there is an extensive ambiguity related to
gauge-fixing dependence. As a result, physical interpretation of these
equations is not universal unlike we treat $\epsilon$ as a small parameter. In
the sector of essential couplings one can find a number of new fixed points,
some of them have no analogs in the $n=4$ case.
