PiRank: Learning To Rank via Differentiable Sorting

A key challenge with machine learning approaches for ranking is the gap between the performance metrics of interest and the surrogate loss functions that can be optimized with gradient-based methods. This gap arises because ranking metrics typically involve a sorting operation which is not differentiable w.r.t. the model parameters. Prior works have proposed surrogates that are loosely related to ranking metrics or simple smoothed versions thereof. We propose PiRank, a new class of differentiable surrogates for ranking, which employ a continuous, temperature-controlled relaxation to the sorting operator. We show that PiRank exactly recovers the desired metrics in the limit of zero temperature and scales favorably with the problem size, both in theory and practice. Empirically, we demonstrate that PiRank significantly improves over existing approaches on publicly available internet-scale learning-to-rank benchmarks.