On the Minimax Regret in Online Ranking with Top-k Feedback

TL;DR

This paper characterizes the minimax regret rates in online ranking with top-k feedback for various performance measures and provides an efficient algorithm for Precision@n.

Contribution

It offers a complete characterization of minimax regret rates for all k and key ranking measures, solving open problems from prior work.

Findings

Full regret rate characterization for Pairwise Loss, DCG, and P@n.

Efficient algorithm achieving minimax regret for P@n.

Analysis extends understanding of partial feedback in online ranking.

Abstract

In online ranking, a learning algorithm sequentially ranks a set of items and receives feedback on its ranking in the form of relevance scores. Since obtaining relevance scores typically involves human annotation, it is of great interest to consider a partial feedback setting where feedback is restricted to the top-$k$ items in the rankings. Chaudhuri and Tewari [2017] developed a framework to analyze online ranking algorithms with top $k$ feedback. A key element in their work was the use of techniques from partial monitoring. In this paper, we further investigate online ranking with top $k$ feedback and solve some open problems posed by Chaudhuri and Tewari [2017]. We provide a full characterization of minimax regret rates with the top $k$ feedback model for all $k$ and for the following ranking performance measures: Pairwise Loss, Discounted Cumulative Gain, and Precision@n. In addition, we give an efficient algorithm that achieves the minimax regret rate for Precision@n.