Optimal Interventions on the Linear Threshold Model in Large-Scale Networks

TL;DR

This paper develops a scalable approximation method for optimal interventions in the linear threshold model on large networks, using mean-field theory and linear programming.

Contribution

It introduces a novel linear programming approach based on mean-field approximation for large-scale network interventions with limited network knowledge.

Findings

The method performs well on real-world networks.

It provides near-optimal solutions compared to existing algorithms.

Abstract

We study an optimal intervention problem on the linear threshold model (LTM) in which a social planner aims to design minimal-cost interventions that modify the agents' thresholds, under the constraint that at least a predefined fraction of agents reaches a given state after a finite number of iterations. While this problem is known to be NP-hard and its exact solution requires full knowledge of the network structure, we focus on approximate solutions for large-scale networks and assume that the planner has only statistical knowledge of the network. In particular, we build on a local mean-field approximation of the LTM that is known to hold true on large-scale random networks, and reformulate the optimal intervention problem as a linear program with an infinite set of constraints. We then show how to approximate the solutions of the latter problem by standard linear programs with finitely many constraints. Finally, our approach is validated through numerical experiments on real-world networks and compared both with optimal seeding and state-of-the-art algorithms for the least-cost influence.