An Invex Relaxation Approach for Minimizing Polarization from Fully and Partially Observed Initial Opinions

Meher Chaitanya, Adarsh Barik, Mansi Rankawat, Jean Honorio

Primary Area: general machine learning (i.e., none of the above)

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Keywords: Polarization, Friedkin-Johnson dynamics, Social Networks, Opinion Dynamics

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TL;DR: A Nonconvex Relaxation Approach for Minimizing Polarization under Friedkin-Johnson dynamics for Fully and Partially Observed Initial Opinions on Social Networks

Abstract: This paper investigates the problem of minimizing polarization within a network, operating under the foundational assumption that the evolution of underlying opinions adheres to the most prevalent model, the Friedkin-Johnson (FJ) model. We show that this optimization problem under integrality constraints is $\mathcal{NP}$-Hard. Furthermore, we establish that the objective function fits into a specialized category of nonconvex functions called invex, where every local minimum is a global minimum. We extend this characterization to encompass a comprehensive class of matrix functions, including those pertinent to polarization and multiperiod polarization, even when addressing scenarios involving stubborn actors. We propose a novel nonconvex framework for this class of matrix functions with theoretical guarantees and demonstrate its practical efficacy for minimizing polarization without getting stuck at local minima. Through empirical assessments conducted in real-world network scenarios, our proposed approach consistently outperforms existing state-of-the-art methodologies. Moreover, we extend our work to encompass a novel problem setting that has not been previously studied, wherein the observer possesses access solely to a subset of initial opinions. Within this agnostic framework, we introduce a nonconvex relaxation methodology, which provides similar theoretical guarantees as outlined earlier and effectively mitigates polarization.

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Submission Number: 6576