TopRank+: A Refinement of TopRank Algorithm

TL;DR

This paper refines the TopRank algorithm for online learning to rank by introducing tighter bounds using advanced mathematical techniques, leading to improved algorithm performance and more accurate regret estimation.

Contribution

It presents a novel refinement of the TopRank algorithm by applying the method of mixtures and asymptotic expansions to achieve tighter theoretical bounds.

Findings

Tighter regret bounds achieved with the refined algorithm.

Improved performance estimation accuracy.

Enhanced theoretical guarantees for online ranking algorithms.

Abstract

Online learning to rank is a core problem in machine learning. In Lattimore et al. (2018), a novel online learning algorithm was proposed based on topological sorting. In the paper they provided a set of self-normalized inequalities (a) in the algorithm as a criterion in iterations and (b) to provide an upper bound for cumulative regret, which is a measure of algorithm performance. In this work, we utilized method of mixtures and asymptotic expansions of certain implicit function to provide a tighter, iterated-log-like boundary for the inequalities, and as a consequence improve both the algorithm itself as well as its performance estimation.