Most antibodies for treating COVID-19 rely on binding the receptor-binding domain (RBD) of SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2). However, Omicron and its sub-lineages, as well as other heavily mutated variants, have rendered many neutralizing antibodies ineffective. Here we show that antibodies with enhanced resistance to the evolution of SARS-CoV-2 can be identified via deep mutational learning. We constructed a library of full-length RBDs of Omicron BA.1 with high mutational distance and screened it for binding to the angiotensin-converting-enzyme-2 receptor and to neutralizing antibodies. After deep-sequencing the library, we used the data to train ensemble deep-learning models for the prediction of the binding and escape of a panel of eight therapeutic antibody candidates targeting a diverse range of RBD epitopes. By using in silico evolution to assess antibody breadth via the prediction of the binding and escape of the antibodies to millions of Omicron sequences, we found combinations of two antibodies with enhanced and complementary resistance to viral evolution. Deep learning may enable the development of therapeutic antibodies that remain effective against future SARS-CoV-2 variants.