Understanding a celltextquoterights expression response to genetic perturbations helps to address important challenges in biology and medicine, including the function of gene circuits, discovery of therapeutic targets and cell reprogramming and engineering. In recent years, Perturb-seq, pooled genetic screens with single cell RNA-seq (scRNA-seq) readouts, has emerged as a common method to collect such data. However, irrespective of technological advances, because combinations of gene perturbations can have unpredictable, non-additive effects, the number of experimental configurations far exceeds experimental capacity, and for certain cases, the number of available cells. While recent machine learning models, trained on existing Perturb-seq data sets, can predict perturbation outcomes with some degree of accuracy, they are currently limited by sub-optimal training set selection and the small number of cell contexts of training data, leading to poor predictions for unexplored parts of perturbation space. As biologists deploy Perturb-seq across diverse biological systems, there is an enormous need for algorithms to guide iterative experiments while exploring the large space of possible perturbations and their combinations. Here, we propose a sequential approach for designing Perturb-seq experiments that uses the model to strategically select the most informative perturbations at each step for subsequent experiments. This enables a significantly more efficient exploration of the perturbation space, while predicting the effect of the rest of the unseen perturbations with high-fidelity. Analysis of a previous large-scale Perturb-seq experiment reveals that our setting is severely restricted by the number of examples and rounds, falling into a non-conventional active learning regime called “active learning on a budget”. Motivated by this insight, we develop IterPert, a novel active learning method that exploits rich and multi-modal prior knowledge in order to efficiently guide the selection of subsequent perturbations. Using prior knowledge for this task is novel, and crucial for successful active learning on a budget. We validate IterPert using insilico benchmarking of active learning, constructed from a large-scale CRISPRi Perturb-seq data set. We find that IterPert outperforms other active learning strategies by reaching comparable accuracy at only a third of the number of perturbations profiled as the next best method. Overall, our results demonstrate the potential of sequentially designing perturbation screens through IterPert.