  User engagement in online social networking depends critically on the level
of social activity in the corresponding platform--the number of online actions,
such as posts, shares or replies, taken by their users. Can we design
data-driven algorithms to increase social activity? At a user level, such
algorithms may increase activity by helping users decide when to take an action
to be more likely to be noticed by their peers. At a network level, they may
increase activity by incentivizing a few influential users to take more
actions, which in turn will trigger additional actions by other users. In this
paper, we model social activity using the framework of marked temporal point
processes, derive an alternate representation of these processes using
stochastic differential equations (SDEs) with jumps and, exploiting this
alternate representation, develop two efficient online algorithms with provable
guarantees to steer social activity both at a user and at a network level. In
doing so, we establish a previously unexplored connection between optimal
control of jump SDEs and doubly stochastic marked temporal point processes,
which is of independent interest. Finally, we experiment both with synthetic
and real data gathered from Twitter and show that our algorithms consistently
steer social activity more effectively than the state of the art.
