Selective Sampling with Almost Optimal Guarantees for Learning to Rank from Pairwise Preferences

One of the practical obstacles of learning to rank from pairwise preference labels is in its (apparent) quadric sample complexity. Some heuristics have been tested for overriding this obstacle. In this workshop we will present new provable method for reducing this sample-complexity, almost reaching the informational lower bound, while suffering only negligible sacrifice of optimality. Our main results: (1) We define a novel structural property of function spaces endowed with a metric loss function that allows searching at an exponential rate. (2) We demonstrate that this structural property applies to the search space arising in the problem of learning to rank from pairwise preferences. As a result, we show that O(npoly(log n, ε−1)) adaptively sampled preferences suffice in order to obtain a ranking of ε · OPT regret, where OPT is loss of the optimal ranking. This is near-optimal in terms of information theory. (3) We show how our algorithm can be used to construct a query-efficient version of the famous SVM-rank relaxation, when the set of points are endowed with feature vectors and we are searching in the restricted space of linear permutations. (4) For feature spaces with a fixed dimension, we show an additional slight improvement in the query complexity using advanced tools from computational geometry.