  We show that an appropriate description of the non-equilibrium dynamics of
disordered systems is obtained through a strong disorder renormalization
procedure in {\it configuration space}, that we define for any master equation
with transitions rates $W ({\cal C} \to {\cal C}')$ between configurations. The
idea is to eliminate iteratively the configuration with the highest exit rate
$W_{out} ({\cal C})= \sum_{{\cal C}'} W ({\cal C} \to {\cal C}')$ to obtain
renormalized transition rates between the remaining configurations. The
multiplicative structure of the new generated transition rates suggests that,
for a very broad class of disordered systems, the distribution of renormalized
exit barriers defined as $B_{out} ({\cal C}) \equiv - \ln W_{out}({\cal C})$
will become broader and broader upon iteration, so that the strong disorder
renormalization procedure should become asymptotically exact at large time
scales. We have checked numerically this scenario for the non-equilibrium
dynamics of a directed polymer in a two dimensional random medium.
