WassRank: Listwise Document Ranking Using Optimal Transport Theory

Learning to rank has been intensively studied and has shown great value in many fields, such as web search, question answering and recommender systems. This paper focuses on listwise document ranking, where all documents associated with the same query in the training data are used as the input. We propose a novel ranking method, referred to as WassRank, under which the problem of listwise document ranking boils down to the task of learning the optimal ranking function that achieves the minimum Wasserstein distance. Specifically, given the query level predictions and the ground truth labels, we first map them into two probability vectors. Analogous to the optimal transport problem, we view each probability vector as a pile of relevance mass with peaks indicating higher relevance. The listwise ranking loss is formulated as the minimum cost (the Wasserstein distance) of transporting (or reshaping) the pile of predicted relevance mass so that it matches the pile of ground-truth relevance mass. The smaller the Wasserstein distance is, the closer the prediction gets to the ground-truth. To better capture the inherent relevance-based order information among documents with different relevance labels and lower the variance of predictions for documents with the same relevance label, ranking-specific cost matrix is imposed. To validate the effectiveness of WassRank, we conduct a series of experiments on two benchmark collections. The experimental results demonstrate that: compared with four non-trivial listwise ranking methods (i.e., LambdaRank, ListNet, ListMLE and ApxNDCG), WassRank can achieve substantially improved performance in terms of nDCG and ERR across different rank positions. Specifically, the maximum improvements of WassRank over LambdaRank, ListNet, ListMLE and ApxNDCG in terms of nDCG@1 are 15%, 5%, 7%, 5%, respectively.