  Biases in existing datasets used to train algorithmic decision rules can
raise ethical and economic concerns due to the resulting disparate treatment of
different groups. We propose an algorithm for sequentially debiasing such
datasets through adaptive and bounded exploration in a classification problem
with costly and censored feedback. Exploration in this context means that at
times, and to a judiciously-chosen extent, the decision maker deviates from its
(current) loss-minimizing rule, and instead accepts some individuals that would
otherwise be rejected, so as to reduce statistical data biases. Our proposed
algorithm includes parameters that can be used to balance between the ultimate
goal of removing data biases -- which will in turn lead to more accurate and
fair decisions, and the exploration risks incurred to achieve this goal. We
analytically show that such exploration can help debias data in certain
distributions. We further investigate how fairness criteria can work in
conjunction with our data debiasing algorithm. We illustrate the performance of
our algorithm using experiments on synthetic and real-world datasets.
