The discovery of the Higgs boson (H) constitutes a tremendous success for the standard model (SM) of particle physics. A crucial property of the Higgs boson is its ability to interact with itself, at a strength precisely predicted by the SM. Measuring this interaction strength is essential to consolidate our understanding of the cornerstone of the mechanism of spontaneous symmetry breaking. The most direct way to access this interaction is to observe the simultaneous production of two Higgs boson (HH) in the collisions of protons provided by the CERN Large Hadron Collider (LHC). Furthermore, there are reasons to believe that the SM is not a complete description of the fundamental particles and interactions. While in the SM, HH production is so rare that it is not expected to be discovered soon, in many scenarios extending the SM its rate can be enhanced to observable levels. This can be due to deviations of the Higgs boson's couplings from SM predictions, or to the production of a new heavy particle X that decays to HH. We present a search for the production of Higgs boson pairs, where one H decays to a pair of b quarks, and the other to a pair of vector bosons which themselves decay to two charged leptons and two neutrinos, in data collected at a centre-of-mass energy of 13 TeV by the CMS experiment at the LHC. The novel technique of parameterised classifiers is used to ensure an optimal sensitivity to the signal for all considered hypotheses. The data are found to be compatible with SM predictions, and limits are set on the cross section of resonant HH production as a function of the mass of the resonance X, and nonresonant HH production as a function of the strength of the Higgs boson self-coupling and of the coupling between the Higgs boson and the top quark.