Network manipulation algorithm based on inexact alternating minimization

TL;DR

This paper introduces an inexact alternating minimization algorithm for network manipulation that accounts for agent errors and organizational credibility, improving convergence and accuracy in network dynamics modeling.

Contribution

It extends existing algorithms to handle inexact solutions, incorporating agent errors and credibility factors, with theoretical analysis of convergence behavior.

Findings

Parameters like agent error and credibility significantly affect convergence.

The algorithm achieves faster convergence with better accuracy under certain conditions.

Mathematically, the approach induces strong convexity, enhancing stability.

Abstract

In this paper, we present a network manipulation algorithm based on an alternating minimization scheme from (Nesterov 2020). In our context, the latter mimics the natural behavior of agents and organizations operating on a network. By selecting starting distributions, the organizations determine the short-term dynamics of the network. While choosing an organization in accordance with their manipulation goals, agents are prone to errors. This rational inattentive behavior leads to discrete choice probabilities. We extend the analysis of our algorithm to the inexact case, where the corresponding subproblems can only be solved with numerical inaccuracies. The parameters reflecting the imperfect behavior of agents and the credibility of organizations, as well as the condition number of the network transition matrix have a significant impact on the convergence of our algorithm. Namely, they turn out not only to improve the rate of convergence, but also to reduce the accumulated errors. From the mathematical perspective, this is due to the induced strong convexity of an appropriate potential function.