Consistency is an important property in dynamic submodular maximization and entails maintaining a near-optimal solution at all times, making only a small number of adjustments to the solution in each step. Prior work has explored this question for the insertion-only case, where the algorithm faces a stream of $n$ insertions, and has established lower and upper bounds for the cardinality-constrained version of the problem. We consider this question in the fully dynamic setting, where the stream of operations may contain both insertions and deletions. We develop a general framework for designing algorithms for this setting, and instantiate it to obtain the first constant-factor approximations with sublinear consistency. For cardinality constraints, we propose a $\frac 12 - O(\varepsilon)$ approximation that is $O\left(\frac{1}{\varepsilon^2}\right)$ consistent. For rank-$k$ matroid constraints, we construct a $\frac 14 - O(\varepsilon)$ approximation to the dynamic optimum that is $O\left(\frac{\log k}{\varepsilon^2}\right)$ consistent.

We present a budget pacing feature called Smart Fast Finish (SFF). SFF builds upon the industry standard Fast Finish (FF) feature in budget pacing systems that depletes remaining advertising budget as quickly as possible towards the end of some fixed time period. SFF dynamically updates system parameters such as start time and throttle rate depending on historical ad-campaign data. SFF is currently in use at DoorDash, one of the largest delivery platforms in the US, and is part of its budget pacing system. We show via online budget-split experimentation data and offline simulations that SFF is a robust solution for overdelivery mitigation when pacing budget.