Noise-Tolerant Interactive Learning Using Pairwise Comparisons

We study the problem of interactively learning a binary classifier using noisylabeling and pairwise comparison oracles, where the comparison oracle answerswhich one in the given two instances is more likely to be positive. Learning fromsuch oracles has multiple applications where obtaining direct labels is harder butpairwise comparisons are easier, and the algorithm can leverage both types oforacles. In this paper, we attempt to characterize how the access to an easiercomparison oracle helps in improving the label and total query complexity. Weshow that the comparison oracle reduces the learning problem to that of learning athreshold function. We then present an algorithm that interactively queries the labeland comparison oracles and we characterize its query complexity under Tsybakovand adversarial noise conditions for the comparison and labeling oracles. Our lowerbounds show that our label and total query complexity is almost optimal.