In this paper, we study the \underline{R}obust \underline{o}ptimization for \underline{se}quence \underline{Net}worked \underline{s}ubmodular maximization (RoseNets) problem. We interweave the robust optimization with the sequence networked submodular maximization. The elements are connected by a directed acyclic graph and the objective function is not submodular on the elements but on the edges in the graph. Under such networked submodular scenario, the impact of removing an element from a sequence depends both on its position in the sequence and in the network. This makes the existing robust algorithms inapplicable. In this paper, we take the first step to study the RoseNets problem. We design a robust greedy algorithm, which is robust against the removal of an arbitrary subset of the selected elements. The approximation ratio of the algorithm depends both on the number of the removed elements and the network topology. We further conduct experiments on real applications of recommendation and link prediction. The experimental results demonstrate the effectiveness of the proposed algorithm.

翻译：本文研究鲁棒序列网络化子模最大化（RoseNets）问题。我们将鲁棒优化与序列网络化子模最大化相结合。各元素通过有向无环图连接，目标函数并非定义在元素上，而是定义在图的边上。在此类网络化子模场景下，从序列中移除一个元素的影响既取决于其在序列中的位置，也取决于其在网络中的位置。这一特性使得现有鲁棒算法不再适用。本文首次对RoseNets问题展开研究。我们设计了一种鲁棒贪心算法，该算法能够抵抗已选元素中任意子集的移除。算法的近似比同时取决于被移除元素的数量和网络拓扑结构。我们进一步在推荐和链接预测等实际应用上开展实验，实验结果证明了所提出算法的有效性。