In multiple domains, actively acquiring missing input information at a reasonable cost in order to improve our understanding of the input–output relationships is of increasing importance. This problem has gained prominence in healthcare, public policy making, education, and in the targeted advertising industry which tries to best match people to products. In this paper we tackle an important variant of this problem: Instance completion, where we want to choose the best k incomplete instances to query from a much larger universe of N ($$\gg $$≫k) incomplete instances so as to learn the most accurate classifier. We propose a principled framework which motivates a generally applicable yet efficient meta-technique for choosing k such instances. Since we cannot know a priori the classifier that will result from the completed dataset, i.e. the final classifier, our method chooses the k instances based on a derived upper bound on the expectation of the distance between the next classifier and the final classifier. We additionally derive a sufficient condition for these two solutions to match. We then empirically evaluate the performance of our method relative to the state-of-the-art methods on four UCI datasets as well as three proprietary e-commerce datasets used in previous studies. In these experiments, we also demonstrate how close we are likely to be to the optimal solution, by quantifying the extent to which our sufficient condition is satisfied. Lastly, we show that our method is easily extensible to the setting where we have a non-uniform cost associated with acquiring the missing information.