Recent technological advances have introduced new high-throughput methods for studying host-virus interactions, but testing synergistic interactions between host gene pairs during infection remains relatively slow and labor intensive. Identification of multiple gene knockdowns that effectively inhibit viral replication requires a search over the combinatorial space of all possible target gene pairs and is infeasible via brute-force experiments. Although active learning methods for sequential experimental design have shown promise, existing approaches have generally been restricted to single-gene knockdowns or small-scale double knockdown datasets. In this study, we present an integrated Deep Active Learning (DeepAL) framework that incorporates information from a biological knowledge graph (SPOKE, the Scalable Precision Medicine Open Knowledge Engine) to efficiently search the configuration space of a large dataset of all pairwise knockdowns of 356 human genes in HIV infection. Through graph representation learning, the framework is able to generate task-specific representations of genes while also balancing the exploration-exploitation trade-off to pinpoint highly effective double-knockdown pairs. We additionally present an ensemble method for uncertainty quantification and an interpretation of the gene pairs selected by our algorithm via pathway analysis. To our knowledge, this is the first work to show promising results on double-gene knockdown experimental data of appreciable scale (356 by 356 matrix).