Submodular maximization over a matroid constraint is a fundamental problem with various applications in machine learning. Some of these applications involve decision-making over datapoints with sensitive attributes such as gender or race. In such settings, it is crucial to guarantee that the selected solution is fairly distributed with respect to this attribute. Recently, fairness has been investigated in submodular maximization under a cardinality constraint in both the streaming and offline settings, however the more general problem with matroid constraint has only been considered in the streaming setting and only for monotone objectives. This work fills this gap. We propose various algorithms and impossibility results offering different trade-offs between quality, fairness, and generality.

翻译：子模最大化在拟阵约束下是一个基础性问题，在机器学习中具有多种应用。其中部分应用涉及对包含敏感属性（如性别或种族）的数据点进行决策。在此类场景中，确保所选解在该属性上公平分布至关重要。近期，公平性已在基数约束下的子模最大化问题中得到研究（涵盖流式与离线两种场景），但更一般的拟阵约束问题仅针对单调目标函数在流式场景中被探讨。本研究填补了该空白。我们提出了多种算法以及不可能性结果，在质量、公平性与通用性之间提供了不同权衡方案。