Graph Reinforcement Learning for Exploring BSM Model Spaces

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.