Abstract The precise targeting of antibodies and other protein therapeutics is required for their proper function and the elimination of deleterious off-target effects. Often the molecular structure of a therapeutic target is unknown and randomized methods are used to design antibodies without a model that relates antibody sequence to desired properties. Here we present a machine learning method that can design human Immunoglobulin G (IgG) antibodies with target affinities that are superior to candidates from phage display panning experiments within a limited design budget. We also demonstrate that machine learning can improve target-specificity by the modular composition of models from different experimental campaigns, enabling a new integrative approach to improving target specificity. Our results suggest a new path for the discovery of therapeutic molecules by demonstrating that predictive and differentiable models of antibody binding can be learned from high-throughput experimental data without the need for target structural data. Significance Antibody based therapeutics must meet both affinity and specificity metrics, and existing in vitro methods for meeting these metrics are based upon randomization and empirical testing. We demonstrate that with sufficient target-specific training data machine learning can suggest novel antibody variable domain sequences that are superior to those observed during training. Our machine learning method does not require any target structural information. We further show that data from disparate antibody campaigns can be combined by machine learning to improve antibody specificity.