  Extending the Standard Model (SM) by a $U(1)_{L_\mu-L_\tau}$ group gives
potentially significant new contributions to $g_\mu-2$, allows the construction
of realistic neutrino mass matrices, incorporates lepton universality
violation, and offers an anomaly-free mediator for a Dark Matter (DM) sector.
In a recent analysis we showed that published LHC searches are not very
sensitive to this model. Here we apply several Machine Learning (ML) algorithms
in order to distinguish this model from the SM using simulated LHC data. In
particular, we optimize the $3\mu$-signal, which has a considerably larger
cross section than the $4\mu$-signal. Furthermore, since the $2$-muon plus
missing $E_T$ final state gets contributions from diagrams involving DM
particles, we optimize it as well. We find greatly improved sensitivity, which
already for $36$ fb$^{-1}$ of data exceeds the combination of published LHC and
non-LHC results. We also emphasize the usefulness of Boosted Decision Trees
which, unlike Neural Networks, easily allow to extract additional information
from the data which directly connect to the theoretical model through feature
importance. The same scheme could be used to analyze other models.
