The objective of a two-stage submodular maximization problem is to reduce the ground set using provided training functions that are submodular, with the aim of ensuring that optimizing new objective functions over the reduced ground set yields results comparable to those obtained over the original ground set. This problem has applications in various domains including data summarization. Existing studies often assume the monotonicity of the objective function, whereas our work pioneers the extension of this research to accommodate non-monotone submodular functions. We have introduced the first constant-factor approximation algorithms for this more general case.

翻译：两阶段子模最大化问题的目标是通过使用提供的子模训练函数来缩减基础集，旨在确保在缩减后的基础集上优化新的目标函数所得到的结果与在原始基础集上获得的结果相当。该问题在数据摘要等多个领域具有应用。现有研究通常假设目标函数具有单调性，而我们的工作率先将该研究扩展至适用于非单调子模函数。针对这一更一般的情况，我们首次引入了常数因子近似算法。