  We present a methodology for performing scans of BSM parameter spaces with
reinforcement learning (RL). We identify a novel procedure using graph neural
networks that is capable of exploring spaces of models without the user
specifying a fixed particle content, allowing broad classes of BSM models to be
explored. In theory, the technique is applicable to nearly any model space with
a pre-specified gauge group. We provide a generic procedure by which a suitable
graph grammar can be developed for any BSM model which features user-specified
symmetry groups and a finite number of different possible particle species. As
a proof of concept, we construct the graph grammar for theories with
vector-like leptons that may or may not be charged under a dark U(1) group,
inspired by portal matter extensions of the sub-GeV vector portal/kinetic
mixing simplified dark matter models. We then use this graph grammar to create
a RL environment tasked with creating models with these vector-like leptons
that are consistent with a list of a variety of precision observables. The RL
agent succeeds in developing models that can address the observed muon
anomalous magnetic moment discrepancy while remaining consistent with flavor
violation and electroweak precision observables, including both constructions
that have previously been studied as well as new models which have not, to our
knowledge, previously been identified. By inspecting the resulting ensembles of
models that the agent produces and experimenting with different configurations
for our RL environment and graph grammar, we also infer various lessons about
the development of these environments that can be transferable to RL scans of
more complicated model spaces, and comment on future directions for the
development of this technique into a more mature tool.
