Ranking with submodular functions on the fly

TL;DR

This paper extends the maximum submodular ranking framework to streaming models, proposing algorithms for function and item arriving scenarios, with applications and empirical evaluations for sequence-ranking problems under constraints.

Contribution

It introduces streaming algorithms for MSR with function and item arriving models, broadening applicability and including constraints like matroids for fair exposure.

Findings

Proposed practical approximation algorithms for streaming MSR.

Extended MSR framework to include constraints such as matroids.

Empirical evaluation demonstrating effectiveness of the algorithms.

Abstract

Maximizing submodular functions have been studied extensively for a wide range of subset-selection problems. However, much less attention has been given to the role of submodularity in sequence-selection and ranking problems. A recently-introduced framework, named \emph{maximum submodular ranking} (MSR), tackles a family of ranking problems that arise naturally when resources are shared among multiple demands with different budgets. For example, the MSR framework can be used to rank web pages for multiple user intents. In this paper, we extend the MSR framework in the streaming setting. In particular, we consider two different streaming models and we propose practical approximation algorithms. In the first streaming model, called \emph{function arriving}, we assume that submodular functions (demands) arrive continuously in a stream, while in the second model, called \emph{item arriving}, we assume that items (resources) arrive continuously. Furthermore, we study the MSR problem with additional constraints on the output sequence, such as a matroid constraint that can ensure fair exposure among items from different groups. These extensions significantly broaden the range of problems that can be captured by the MSR framework. On the practical side, we develop several novel applications based on the MSR formulation, and empirically evaluate the performance of the proposed~methods.