  Machine learning models trained on uncurated datasets can often end up
adversely affecting inputs belonging to underrepresented groups. To address
this issue, we consider the problem of adaptively constructing training sets
which allow us to learn classifiers that are fair in a minimax sense. We first
propose an adaptive sampling algorithm based on the principle of optimism, and
derive theoretical bounds on its performance. We also propose heuristic
extensions of this algorithm suitable for application to large scale, practical
problems. Next, by deriving algorithm independent lower-bounds for a specific
class of problems, we show that the performance achieved by our adaptive scheme
cannot be improved in general. We then validate the benefits of adaptively
constructing training sets via experiments on synthetic tasks with logistic
regression classifiers, as well as on several real-world tasks using
convolutional neural networks (CNNs).
