Combinatorial CRISPR screening enables large-scale identification of synergistic gene pairs for combination therapies, but exhaustive experimentation is infeasible. We introduce NAIAD, an active learning framework that efficiently discovers optimal gene pairs by leveraging single-gene perturbation effects and adaptive gene embeddings that scale with the training data size, mitigating overfitting in small-sample learning while capturing complex gene interactions as more data is collected. Evaluated on four CRISPR datasets with over 350,000 interactions, NAIAD trained on small datasets outperforms existing models by up to 40%. Its recommendation system prioritizes gene pairs with maximum predicted effects, accelerating discovery with fewer experiments. We also extend NAIAD to optimal drug combination identification among 2,000 candidates. Overall, NAIAD enhances combinatorial perturbation design and drives advances in genomics research and therapeutic development in combination therapy. Our code is publicly available at: https://github.com/NeptuneBio/NAIAD