User engagement in social networks depends critically on the number of online
actions their users take in the network. Can we design an algorithm that finds
when to incentivize users to take actions to maximize the overall activity in a
social network? In this paper, we model the number of online actions over time
using multidimensional Hawkes processes, derive an alternate representation of
these processes based on stochastic differential equations (SDEs) with jumps
and, exploiting this alternate representation, address the above question from
the perspective of stochastic optimal control of SDEs with jumps. We find that
the optimal level of incentivized actions depends linearly on the current level
of overall actions. Moreover, the coefficients of this linear relationship can
be found by solving a matrix Riccati differential equation, which can be solved
efficiently, and a first order differential equation, which has a closed form
solution. As a result, we are able to design an efficient online algorithm,
Cheshire, to sample the optimal times of the users' incentivized actions.
Experiments on both synthetic and real data gathered from Twitter show that our
algorithm is able to consistently maximize the number of online actions more
effectively than the state of the art.

本研究探究了如何通过设计在线算法，基于多维 Hawkes 过程的随机微分方程，创新性提出了一种动态激励策略，可最大化社交网络的整体活动，实验数据表明，这种算法能够比现有技术更有效地提高在线活动数量，特别是在推特等真实数据收集的平台上。