The P-Norm Push: A Simple Convex Ranking Algorithm that Concentrates at the Top of the List

Abstract

We are interested in supervised ranking algorithms that perform especially well near the top of the ranked list, and are only required to perform sufficiently well on the rest of the list. In this work, we provide a general form of convex objective that gives high-scoring examples more importance. This “push” near the top of the list can be chosen arbitrarily large or small, based on the preference of the user. We choose ℓp-norms to provide a specific type of push; if the user sets p larger, the objective concentrates harder on the top of the list. We derive a generalization bound based on the p-norm objective, working around the natural asymmetry of the problem. We then derive a boosting-style algorithm for the problem of ranking with a push at the top. The usefulness of the algorithm is illustrated through experiments on repository data. We prove that the minimizer of the algorithm’s objective is unique in a specific sense. Furthermore, we illustrate how our objective is related to quality measurements for information retrieval.