A practical divide-and-conquer approach for preference-based learning to rank

Preference-based learning to rank (LTR) is a model that learns the underlying pairwise preference with soft binary classification, and then ranks test instances based on pairwise preference predictions. The model can be viewed as an alternative to the popular score-based LTR model, which learns a scoring function and ranks test instances based on their scores directly. Many existing works on preference-based LTR address the step of ranking test instances as the problem of weighted minimum feedback arcset on tournament graph. The problem is somehow NP-hard to solve and existing algorithms cannot efficiently produce a decent solution. We propose a practical algorithm to speed up the ranking step while maintaining ranking accuracy. The algorithm employs a divide-and-conquer strategy that mimics merge-sort, and its time complexity is relatively low when compared to other preference-based LTR algorithms. Empirical results demonstrate that the accuracy of the proposed algorithm is competitive to state-of-the-art score-based LTR algorithms.