Interactive Linear Regression with Pairwise Comparisons

A general goal of interactive learning is to investigate broad ways of leveraging human feedback, and understand the benefits of learning from potentially complex feedback. We study a special case of linear regression with access to comparisons between pairs of samples. Learning from such queries is motivated by several important applications, where obtaining comparisons can be much easier than direct labels, and/or when comparisons can be more reliable. We develop an interactive algorithm that utilizes both labels and comparisons to obtain a linear estimator, and show that it only requires a very small amount of direct labels to achieve low error. We also give minimax lower bounds for the problem, showing that our algorithm is optimal up to log factors. Finally, experiments show that our algorithm outperforms label-only algorithms when labels are scarce, and it can be practical for real-world applications.