The dynamical processes taking place on a network depend on its topology. Influencing the growth process of a network therefore has important implications on such dynamical processes. We formulate the problem of influencing the growth of a network as a stochastic optimal control problem in which a structural cost function penalizes undesired topologies. We approximate this control problem with a restricted class of control problems that can be solved using probabilistic inference methods. To deal with the increasing problem dimensionality, we introduce an adaptive importance sampling method for approximating the optimal control. We illustrate this methodology in the context of formation of information cascades, considering the task of influencing the structure of a growing conversation thread, as in Internet forums. Using a realistic model of growing trees, we show that our approach can yield conversation threads with better structural properties than the ones observed without control.

This project is co-financed by the Marie Curie FP7-PEOPLE-2012-COFUND Action, Grant agreement no: 600387, the Marie Curie Initial Training Network NETT, project N. 289146 and the Spanish Ministry of Economy and Competitiveness under the Mar´ıa de Maeztu Units of Excellence Programme (MDM-2015-0502).