Mean-field control and deep learning for information dissemination problem in online social networks

The paper formulates and numerically investigates the tasks of stopping and stimulating the dissemination of information in online social networks for a mean-field model and a model based on artificial neural networks.The mean field model is reduced to a joint solution of initial boundary value problems for the Kolmogorov-Fokker-Planck (KFP) and Hamilton-Jacobi-Bellman (HJB) equations, as well as the Nash optimality condition.Numerical methods for solving systems of KFP and HJB in high dimensions are practically nonexistent due to the need for grid-based spatial discretization.Therefore, we propose a deep learning algorithm based on the generative adversarial network.We parameterize the value (the solution of HJB) and density (the solution of KFP) functions by two neural networks that solve a convex-concave saddle-point problem.