Many inference problems in bioinformatics, including drug bioactivity prediction, can be formulated as pairwise learning problems, in which one is interested in making predictions for pairs of objects, e.g. drugs and their targets. Kernel-based approaches have emerged as powerful tools for solving problems of that kind, and especially multiple kernel learning (MKL) offers promising benefits as it enables integrating various types of complex biomedical information sources in the form of kernels, along with learning their importance for the prediction task. However, the immense size of pairwise kernel spaces remains a major bottleneck, making the existing MKL algorithms computationally infeasible even for small number of input pairs.