Randomized Kaczmarz for rank aggregation from pairwise comparisons

We revisit the problem of inferring the overall ranking among entities in the framework of Bradley-Terry-Luce (BTL) model, based on available empirical data on pairwise preferences. By a simple transformation, we can cast the problem as that of solving a noisy linear system, for which a ready algorithm is available in the form of the randomized Kaczmarz method. This scheme is provably convergent and has excellent empirical performance. Convergence, convergence rate, and error analysis of the proposed algorithm are presented and several numerical experiments are conducted whose results validate our theoretical findings.