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.

翻译：在亚模块排名(SR)问题中,输入由一组根据一组地面元素定义的子模块函数组成。目标是尽可能快地命令所有功能的价值均高于某一阈值的元素,假设我们每次选择一个元素。问题足够灵活,足以捕捉机器学习中的各种应用,包括决策树。本文考虑了多个实例共享地面集的微最大SR版本。考虑到每个实例都与一个代理有关,最小模式问题是命令共同元素尽可能减少所有代理的最大目标,从而为所有代理商找到公平的解决办法。我们给出了这一问题的近似算法,并展示了它们在为多个代理商寻找决策树时的有效性。