In dynamic submodular maximization, the goal is to maintain a high-value solution over a sequence of element insertions and deletions with a fast update time. Motivated by large-scale applications and the fact that dynamic data often exhibits patterns, we ask the following question: can predictions be used to accelerate the update time of dynamic submodular maximization algorithms? We consider the model for dynamic algorithms with predictions where predictions regarding the insertion and deletion times of elements can be used for preprocessing. Our main result is an algorithm with an $O(poly(\log \eta, \log w, \log k))$ amortized update time over the sequence of updates that achieves a $1/2 - \epsilon$ approximation in expectation for dynamic monotone submodular maximization under a cardinality constraint $k$, where the prediction error $\eta$ is the number of elements that are not inserted and deleted within $w$ time steps of their predicted insertion and deletion times. This amortized update time is independent of the length of the stream and instead depends on the prediction error.

翻译：在动态子模最大化问题中，目标是在元素插入和删除的序列上维护一个高价值解，并实现快速更新。受大规模应用以及动态数据常呈现模式这一事实的启发，我们提出以下问题：能否利用预测来加速动态子模最大化算法的更新时间？我们考虑带有预测的动态算法模型，其中关于元素插入和删除时间的预测可用于预处理。我们的主要成果是在满足基数约束$k$的动态单调子模最大化问题上，提出一种算法，该算法在更新序列上具有$O(poly(\log \eta, \log w, \log k))$的摊销更新时间，并能达到$1/2 - \epsilon$的期望近似比。其中，预测误差$\eta$指未在预测插入和删除时间前后$w$个时间步内完成插入和删除的元素数量。该摊销更新时间与数据流长度无关，而仅取决于预测误差。