Min-max Submodular Ranking for Multiple Agents

TL;DR

This paper introduces approximation algorithms for the min-max submodular ranking problem involving multiple agents, aiming to fairly order elements to optimize shared submodular functions, with applications in decision tree construction.

Contribution

It presents the first approximation algorithms for the min-max submodular ranking problem with multiple agents, addressing fairness in shared element ordering.

Findings

Algorithms achieve near-optimal fairness in element ordering.

Effective application to multi-agent decision tree construction.

Demonstrated improved approximation ratios over baseline methods.

Abstract

In the submodular ranking (SR) problem, the input consists of a set of submodular functions defined on a ground set of elements. The goal is to order elements for all the functions to have value above a certain threshold as soon on average as possible, assuming we choose one element per time. The problem is flexible enough to capture various applications in machine learning, including decision trees. This paper considers the min-max version of SR where multiple instances share the ground set. With the view of each instance being associated with an agent, the min-max problem is to order the common elements to minimize the maximum objective of all agents -- thus, finding a fair solution for all agents. We give approximation algorithms for this problem and demonstrate their effectiveness in the application of finding a decision tree for multiple agents.