Math-based reinforcement learning for the adaptive budgeted influence maximization problem

In social networks, the influence maximization problem requires selecting an initial set of nodes to influence so that the spread of influence can reach its maximum under certain diffusion models. Usually, the problem is formulated in a two-stage un-budgeted fashion: The decision maker selects a given number of nodes to influence and observes the results. In the adaptive version of the problem, it is possible to select the nodes at each time step of a given time interval. This allows the decision-maker to exploit the observation of the propagation and to make better decisions. This paper considers the adaptive budgeted influence maximization problem, that is, the adaptive problem in which the decision maker has a finite budget to influence the nodes, and each node requires a cost to be influenced. We present two solution techniques: The first is an approximated value iteration leveraging mixed integer linear problems while the second exploits new concepts from graph neural networks. Extensive numerical experiments demonstrate the effectiveness of the proposed approaches.