We present a low-cost, virtual high-throughput materials design workflow and use it to identify earth-abundant materials for solar energy applications from the quaternary oxide chemical space. A statistical model that predicts bandgap from chemical composition is built using supervised machine learning. The trained model forms the first in a hierarchy of screening steps. An ionic substitution algorithm is used to assign crystal structures, and an oxidation state probability model is used to discard unlikely chemistries. We demonstrate the utility of this process for screening over 1 million oxide compositions. We find that, despite the difficulties inherent to identifying stable multicomponent inorganic materials, several compounds produced by our workflow are calculated to be thermodynamically stable or metastable and have desirable optoelectronic properties according to first-principles calculations. The predicted oxides are Li2MnSiO5, MnAg(SeO3)2, and two polymorphs of MnCdGe2O6, all four of which are found to have direct electronic bandgaps in the visible range of the solar spectrum.