  We introduce a Monte Carlo scheme for sampling bold-line diagrammatic series
specifying an unknown function in terms of itself. The range of convergence of
this bold(-line) diagrammatic Monte Carlo (BMC) is significantly broader than
that of a simple iterative scheme for solving integral equations. With BMC
technique, a moderate "sign problem" turns out to be an advantage in terms of
the convergence of the process. For an illustrative example, we solve
one-particle s-scattering problem. As an important application, we obtain
T-matrix for a fermipolaron (one spin-down particle interacting with the
spin-up fermionic sea).
