Hard-Margin Active Linear Regression

We consider the fundamental problem of linear regression in which the designer can actively choose observations. This model naturally captures various experiment design settings in medical experiments, ad placement problems and more. Whereas previous literature addresses the soft-margin or mean-square-error variants of the problem, we consider a natural machine learning hard-margin criterion. In this setting, we show that active learning admits significantly better sample complexity bounds than the passive learning counterpart, and give efficient algorithms that attain near-optimal bounds.