Abstract. An important task in many scientific and engineering disciplines is to set up experiments with the goal of finding the best instances (substances, compositions, designs) as evaluated on an unknown target function using limited resources. We study this problem using machine learning principles, and introduce the novel task of active k-optimization. The problem consists of approximating the k best instances with regard to an unknown function and the learner is active, that is, it can present a limited number of instances to an oracle for obtaining the target value. We also develop an algorithm based on Gaussian processes for tackling active k-optimization, and evaluate it on a challenging set of tasks related to structure-activity relationship prediction. Key words: Active Learning, Chemical compounds, Optimization, QSAR