In this paper, we study a fundamental problem in submodular optimization,
which is called sequential submodular maximization. Specifically, we aim to
select and rank a group of $k$ items from a ground set $V$ such that the
weighted summation of $k$ (possibly non-monotone) submodular functions $f_1,
\cdots ,f_k: 2^V \rightarrow \mathbb{R}^+$ is maximized, here each function
$f_j$ takes the first $j$ items from this sequence as input. The existing
research on sequential submodular maximization has predominantly concentrated
on the monotone setting, assuming that the submodular functions are
non-decreasing. However, in various real-world scenarios, like diversity-aware
recommendation systems, adding items to an existing set might negatively impact
the overall utility. In response, this paper pioneers the examination of the
aforementioned problem with non-monotone submodular functions and offers
effective solutions for both flexible and fixed length constraints, as well as
a special case with identical utility functions. The empirical evaluations
further validate the effectiveness of our proposed algorithms in the domain of
video recommendations. The results of this research have implications in
various fields, including recommendation systems and assortment optimization,
where the ordering of items significantly impacts the overall value obtained.

研究论文中，我们探讨了序列次模优化的基本问题，针对从一个给定集合中选择和排序 k 个项目的场景，最大化 k 个（可能非单调的）次模函数的加权求和，其中每个函数 f_j 将序列中的前 j 个项目作为输入。不同于过去关于单调情形的研究，本文首次考虑了具有非单调次模函数的问题，并提出了对于灵活和固定长度约束以及具有相同效用函数的特殊情况的有效解决方案。通过视频推荐领域的实证评估，我们提出的算法的有效性得到了验证。这项研究的结果对推荐系统和组合优化等多个领域具有重要意义，其中项目的排序对于整体价值具有显著影响。