Cheshire: An Online Algorithm for Activity Maximization in Social Networks

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.

RedQueen: An Online Algorithm for Smart Broadcasting in Social Networks

Users in social networks whose posts stay at the top of their followers'{} feeds the longest time are more likely to be noticed. Can we design an online algorithm to help them decide when to post to stay at the top? In this paper, we address this question as a novel optimal control problem for jump stochastic differential equations. For a wide variety of feed dynamics, we show that the optimal broadcasting intensity for any user is surprisingly simple -- it is given by the position of her most recent post on each of her follower's feeds. As a consequence, we are able to develop a simple and highly efficient online algorithm, RedQueen, to sample the optimal times for the user to post. Experiments on both synthetic and real data gathered from Twitter show that our algorithm is able to consistently make a user's posts more visible over time, is robust to volume changes on her followers' feeds, and significantly outperforms the state of the art.