While over 100 lunar pyroclastic deposits have been identified remotely, their compositions remain poorly constrained. In this work, we determine the compositions of three lunar regional pyroclastic deposits which are likely to contain large amounts of glass and for which we have high-quality ground-based spectra: the Aristarchus Plateau, Mare Humorum, and Sulpicius Gallus. We use radiative transfer theory and employ measured optical constants of glasses to predict the bidirectional reflectance of a particulate glass surface as a function of Fe and Ti concentration, particle size, and maturity in order to find the best spectral match to the remotely observed deposits. Tools are not available to model the optical effects of the unusual geometries of the ilmenite laths in the black beads, so we address their effects on spectra of the regional pyroclastic deposits using computational mixing. We find that model spectra of pure glass (as opposed to devitrified black beads) provide good matches to all three regions. Radiative transfer modeling predicts iron contents of 21, 20, and 17 wt% FeO for Aristarchus, Humorum, and Sulpicius Gallus, respectively, and suggests that all three regions are low in titanium, a result supported by Lunar Prospector neutron spectrometer data. However, we find that a moderate Ti glass mixed with a small fraction of black beads cannot be ruled out for the Sulpicius Gallus region.