  In many industrial applications, obtaining labeled observations is not
straightforward as it often requires the intervention of human experts or the
use of expensive testing equipment. In these circumstances, active learning can
be highly beneficial in suggesting the most informative data points to be used
when fitting a model. Reducing the number of observations needed for model
development alleviates both the computational burden required for training and
the operational expenses related to labeling. Online active learning, in
particular, is useful in high-volume production processes where the decision
about the acquisition of the label for a data point needs to be taken within an
extremely short time frame. However, despite the recent efforts to develop
online active learning strategies, the behavior of these methods in the
presence of outliers has not been thoroughly examined. In this work, we
investigate the performance of online active linear regression in contaminated
data streams. Our study shows that the currently available query strategies are
prone to sample outliers, whose inclusion in the training set eventually
degrades the predictive performance of the models. To address this issue, we
propose a solution that bounds the search area of a conditional D-optimal
algorithm and uses a robust estimator. Our approach strikes a balance between
exploring unseen regions of the input space and protecting against outliers.
Through numerical simulations, we show that the proposed method is effective in
improving the performance of online active learning in the presence of
outliers, thus expanding the potential applications of this powerful tool.
