Ph. D. Project
Theoretical fundations of the viral marketing problem
2021/04/15 - 2024/03/30
In this thesis, we consider the problem of influence maximization (or minimization) over a set of agents linked through a social network. The general goal of the thesis is to know which agents should be targeted and at what degree, so that the influencer reaches as well as possible a given quantitative objective.

The retained approach is theoretical but will be very useful to better understand complex influence phenomena when the problem structure by the presence of a graph. Thanks to our recent research works [1][2], we have been able to identify several fundamental problems. The graph is assumed to be very large, which poses a dimensionality problem that will be tackled by using random matrix theory. The links between the agents are assumed to be stochastic, which will lead us to use tools from probability theory and Bayesian inference. The graph parameters and that of the dynamics will be assumed only partially observable. We will exploit robust control theory to study this aspect. At last, the performance metric of the influencer will be assumed to be imperfectly known.

By putting in synergy tools from random matrix theory, probability theory (mean fields in particular) and robust control theory, the Ph.D student will conduct convergence and stability analyses of a dynamical graph under exogenous influence. The Ph.D student will also conduct sensivity analyses vis-à-vis the degree of randomness, the dimension of the graph, and the observation noise level.

[1] V. S. Varma, S. Lasaulce, J. Mounthanyvong, and I.-C. Morarescu, "Allocating marketing resources
over social networks: A long-term analysis", IEEE Control Systems Letters (L-CSS), Vol.
3, No. 4, pp. 1002-1007, April 2019.

[2] I.-C. Morarescu, V. S. Varma, L. Busoniu, and S. Lasaulce, "Space-time budget allocation policy design for marketing over social networks", IFAC Journal on Nonlinear Analysis: Hybrid Systems (NAHS), Vol. 37, Aug. 2020.
Graph theory, control theory, viral marketing
Control Identification Diagnosis