The bold diagrammatic Monte Carlo (BDMC) method performs an unbiased sampling of Feyn- man's diagrammatic series using skeleton diagrams. For lattice models the eciency of BDMC can be dramatically improved by incorporating dynamic mean-field theory solutions into renormalized propagators. From the DMFT perspective, combining it with BDCM leads to an unbiased method with well-defined accuracy. We illustrate the power of this approach by computing the single-particle propagator (and thus the density of states) in the non-perturbative regime of the Anderson local- ization problem, where a gain of the order of 104 is achieved with respect to conventional BDMC in terms of convergence to the exact answer.