A machine learning strategy is presented for the rapid discovery of new polymeric materials satisfying multiple desirable properties. Of particular interest is the design of high refractive index polymers. Our in silico approach employs a series of quantitative structure–property relationship models that facilitate rapid virtual screening of polymers based on relevant properties such as the refractive index, glass transition and thermal decomposition temperatures, and solubility in standard solvents. Exploration of the chemical space is carried out using an evolutionary algorithm that assembles synthetically tractable monomers from a database of existing fragments. Selected monomer structures that were further evaluated using density functional theory calculations agree well with model predictions.