High-throughput drug combination screening provides a systematic strategy to discover unexpected combinatorial synergies in pre-clinical cell models. However, phenotypic combinatorial screening with multi-dose matrix assays is experimentally expensive, especially when the aim is to identify selective combination synergies across a large panel of cell lines or patient samples. Here we implemented DECREASE, an efficient machine learning model that requires only a limited set of pairwise dose-response measurements for accurate prediction of drug combination synergy and antagonism. Using a compendium of 23,595 drug combination matrices tested in various cancer cell lines, and malaria and Ebola infection models, we demonstrate how cost-effective experimental designs with DECREASE capture almost the same degree of information for synergy and antagonism detection as the fully-measured dose-response matrices. Measuring only the diagonal of the matrix provides an accurate and practical option for combinatorial screening. The open-source web-implementation enables applications of DECREASE to both pre-clinical and translational studies.