In recent years, it has become clear that rankings delivered in many areas need not only be useful to the users but also respect fairness of exposure for the item producers. We consider the problem of finding ranking policies that achieve a Pareto-optimal tradeoff between these two aspects. Several methods were proposed to solve it; for instance a popular one is to use linear programming with a Birkhoff-von Neumann decomposition. These methods, however, are based on a classical Position Based exposure Model (PBM), which assumes independence between the items (hence the exposure only depends on the rank). In many applications, this assumption is unrealistic and the community increasingly moves towards considering other models that include dependences, such as the Dynamic Bayesian Network (DBN) exposure model. For such models, computing (exact) optimal fair ranking policies remains an open question. We answer this question by leveraging a new geometrical method based on the so-called expohedron proposed recently for the PBM (Kletti et al., WSDM'22). We lay out the structure of a new geometrical object (the DBN-expohedron), and propose for it a Carath\'eodory decomposition algorithm of complexity $O(n^3)$, where $n$ is the number of documents to rank. Such an algorithm enables expressing any feasible expected exposure vector as a distribution over at most $n$ rankings; furthermore we show that we can compute the whole set of Pareto-optimal expected exposure vectors with the same complexity $O(n^3)$. Our work constitutes the first exact algorithm able to efficiently find a Pareto-optimal distribution of rankings. It is applicable to a broad range of fairness notions, including classical notions of meritocratic and demographic fairness. We empirically evaluate our method on the TREC2020 and MSLR datasets and compare it to several baselines in terms of Pareto-optimality and speed.
翻译:近年来,在许多领域提供的排名显然不仅需要对用户有用,而且需要尊重物品生产者接触的公平性。我们考虑了在这两个方面找到实现Pareto最佳权衡的排名政策的问题。提出了几种方法解决这个问题;例如,一个流行的方法是使用Birkhoff-von Neumann分解法的线性编程。然而,这些方法基于经典的基于位置的20级暴露模型(PBM),该模型假定在项目之间具有独立性(因为接触仅取决于级别)。在许多应用中,这一假设是不现实的,而且社区越来越多地考虑其他模式,其中包括依赖性,例如动态Bayesian网络(DBNBN) 。对于这些模型,计算(exact)最佳的公平排名政策仍然是一个尚未解决的问题。我们通过利用基于所谓的Excomedoral 20级(PBM) 标准(Wletet and al.,WSDDM'22) 。我们将一个新的直径直径目标的直径直径直值值值值数据结构结构结构(包括DBN-Oxxxxxlent 预估值数据),我们将一个直径直径直径直径的直位值的直值值值的直径直判值值值值值值值值值值值值值值值值值的直值值值值值值值值值值值值值值值值值值值值值值值值值值值值值值值的分布值文件。