  A new, very general, robust procedure for combining estimators in metric
spaces is introduced GROS. The method is reminiscent of the well-known median
of means, as described in \cite{devroye2016sub}. Initially, the sample is
divided into $K$ groups. Subsequently, an estimator is computed for each group.
Finally, these $K$ estimators are combined using a robust procedure. We prove
that this estimator is sub-Gaussian and we get its break-down point, in the
sense of Donoho. The robust procedure involves a minimization problem on a
general metric space, but we show that the same (up to a constant)
sub-Gaussianity is obtained if the minimization is taken over the sample,
making GROS feasible in practice. The performance of GROS is evaluated through
five simulation studies: the first one focuses on classification using
$k$-means, the second one on the multi-armed bandit problem, the third one on
the regression problem. The fourth one is the set estimation problem under a
noisy model. Lastly, we apply GROS to get a robust persistent diagram.
