论文标题
拜占庭光谱排名
Byzantine Spectral Ranking
论文作者
论文摘要
我们研究了等级聚合的问题,目的是通过汇总选民对一组项目的成对比较来获得全球排名。我们考虑一个对抗性环境,将选民分为两组。第一盘以随机分数的Bradley-terry-luce(BTL)模型以随机方式进行投票,以进行成对比较。第二组包括试图恶化排名的恶意拜占庭选民。我们认为拜占庭选民知道BTL得分,好选民的选票,算法,并且可以相互勾结。我们首先表明,基于流行的频谱排名排名算法算法虽然对BTL模型的最佳作用,但即使一小部分选民是拜占庭式的,但表现不佳。我们介绍了拜占庭光谱排名算法(并且是它更快的变体),当优秀选民的数量超过拜占庭选民的数量时,它会产生可靠的排名。我们表明,当拜占庭选民多于好选民时,所有BTL权重> 1/2的概率> 1/2,没有算法可以产生令人满意的排名,这表明我们的算法适用于所有可能的人群分数。我们通过对合成和实际数据集进行实验结果来支持我们的理论结果,以证明在几个对抗场景下排名中心算法的失败,以及拟议的拜占庭频谱排名算法如何强大地获得良好的排名。
We study the problem of rank aggregation where the goal is to obtain a global ranking by aggregating pair-wise comparisons of voters over a set of items. We consider an adversarial setting where the voters are partitioned into two sets. The first set votes in a stochastic manner according to the popular score-based Bradley-Terry-Luce (BTL) model for pairwise comparisons. The second set comprises malicious Byzantine voters trying to deteriorate the ranking. We consider a strongly-adversarial scenario where the Byzantine voters know the BTL scores, the votes of the good voters, the algorithm, and can collude with each other. We first show that the popular spectral ranking based Rank-Centrality algorithm, though optimal for the BTL model, does not perform well even when a small constant fraction of the voters are Byzantine. We introduce the Byzantine Spectral Ranking Algorithm (and a faster variant of it), which produces a reliable ranking when the number of good voters exceeds the number of Byzantine voters. We show that no algorithm can produce a satisfactory ranking with probability > 1/2 for all BTL weights when there are more Byzantine voters than good voters, showing that our algorithm works for all possible population fractions. We support our theoretical results with experimental results on synthetic and real datasets to demonstrate the failure of the Rank-Centrality algorithm under several adversarial scenarios and how the proposed Byzantine Spectral Ranking algorithm is robust in obtaining good rankings.