  We present a technique that enables the evaluation of perturbative expansions
based on one-loop-renormalized vertices up to large expansion orders.
Specifically, we show how to compute large-order corrections to the random
phase approximation in either the particle-hole or particle-particle channels.
The algorithm's efficiency is achieved by the summation over contributions of
all symmetrized Feynman diagram topologies using determinants, and by
integrating out analytically the two-body long-range interactions in order to
yield an effective zero-range interaction. Notably, the exponential scaling of
the algorithm as a function of perturbation order leads to a polynomial scaling
of the approximation error with computational time for a convergent series. To
assess the performance of our approach, we apply it to the non-perturbative
regime of the square-lattice fermionic Hubbard model away from half-filling and
report, as compared to the bare interaction expansion algorithm, significant
improvements of the Monte Carlo variance as well as the convergence properties
of the resulting perturbative series.
