  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.
