Therapeutic antibody design is a complex multi-property optimization problem that traditionally relies on expensive search through sequence space. Here, we introduce Lab-in-the-loop, a paradigm shift for antibody design that orchestrates generative machine learning models, multi-task property predictors, active learning ranking and selection, and in vitro experimentation in a semi-autonomous, iterative optimization loop. By automating the design of antibody variants, property prediction, ranking and selection of designs to assay in the lab, and ingestion of in vitro data, we enable a holistic, end-to-end approach to antibody optimization. We apply lab-in-the-loop to four clinically relevant antigen targets: EGFR, IL-6, HER2, and OSM. Over 1,800 unique antibody variants are designed and tested, derived from lead molecule candidates obtained via animal immunization and state-of-the-art immune repertoire mining techniques. Four lead candidate and four design crystal structures are solved to reveal mechanistic insights into the effects of mutations. We perform four rounds of iterative optimization and report 3-100x better binding variants for every target and ten candidate lead molecules, with the best binders in a therapeutically relevant 100 pM range.