  We describe a stochastic technique which allows one to compute numerically
the coefficients of the weak coupling perturbative expansion of any observable
in Lattice Gauge Theory. The idea is to insert the exponential representation
of the link variables $U_\mu(x) \to \exp\{A_\mu(x)/\sqrt\beta\}$ into the
Langevin algorithm and the observables and to perform the expansion in
\beta^{-1/2}. The Langevin algorithm is converted into an infinite hierarchy of
maps which can be exactly truncated at any order. We give the result for the
simple plaquette of SU(3) up to fourth loop order (\beta^{-4}) which extends by
one loop the previously known series.
