On the Limits of PAC Learning of Networks from Opinion Dynamics

2026-05-14

AI Summary

This study addresses the problem of efficiently learning social network structures from synchronous opinion update samples, particularly in realistic scenarios where parts of the underlying dynamics are unknown. Building upon the threshold-based opinion dynamics model, the work establishes the first Probably Approximately Correct (PAC) learnability framework for network reconstruction: it presents an efficient learning algorithm when the number of influencers is bounded, while proving computational intractability under majority-rule dynamics. Integrating PAC learning theory, computational complexity analysis, and graph-theoretic insights, the authors develop a high-success-rate heuristic reconstruction algorithm that achieves over 98% accuracy on random graphs in simulations and guarantees zero reconstruction failure under specific conditions.

Abstract

Agents in social networks with threshold-based dynamics change opinions when influenced by sufficiently many peers. Existing literature typically assumes that the network structure and dynamics are fully known, which is often unrealistic. In this work, we ask how to learn a network structure from samples of the agents' synchronous opinion updates. Firstly, if the opinion dynamics follow a threshold rule in which a fixed number of influencers prevent opinion change (e.g., unanimity and quasi-unanimity), we provide an efficient PAC learning algorithm provided that the number of influencers per agent is bounded. Secondly, under standard computational complexity assumptions, we prove that if agents' opinions follow the majority of their influencers, then there is no efficient PAC learning algorithm. We propose a polynomial-time heuristic that successfully learns consistent networks in over $98\%$ of our simulations on random graphs, with no failures for some specified conditions on the numbers of agents and opinion diffusion examples.

Problem

• PAC learning
• opinion dynamics
• network structure learning
• threshold rule
• social networks

Innovation

• PAC learning
• opinion dynamics
• threshold rules
• network reconstruction
• computational hardness