Robustness to Dependency in Influence Maximization

In this paper, we pursue a correlation-robust study of the influence maximization problem. Departing from the classic independent cascade model, we study a diffusion process adversarially adapted to the choice of seed set. More precisely, rather than the independent coupling of known individual edge probabilities, we now evaluate a seed set’s expected influence under all possible correlations, specifically, the one that presents the worst case. We find that the worst case expected influence can be efficiently computed, its NP-hard optimization done approximately Formula: see text with greedy construction, and we provide complete, efficient characterizations of the adversarial coupling, the random graph, and the random number of influenced nodes. But, most importantly, upon mixing the independent cascade with the worst case, we attain a tunable and more comprehensive model better suited for real-world diffusion phenomena than the independent cascade alone and without increased computational complexity. Extensions to the correlation-robust study of risk follow along with numerical experiments on network data sets with demonstration of how our models can be tuned. This paper was accepted by George Shanthikumar, data science. Funding: This work was supported by the Air Force Office of Scientific Research (Mathematical Optimization Program) under the grant: “Optimal Decision Making under Tight Performance Requirements in Adversarial and Uncertain Environments: Insight from Rockafellian Functions”. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2021.03445 .