Maximizing Truth Learning in a Social Network is NP-hard

2025-02-18

AI Summary

This paper investigates the problem of optimizing the sequential decision-making order of agents in social networks to maximize the fraction of individuals correctly inferring the true state. Agents observe noisy private signals and local neighborhood actions. The authors establish, for the first time, that computing the optimal ordering is NP-hard under both Bayesian social learning and the simple majority rule—two canonical models—and further prove that no polynomial-time approximation algorithm exists (i.e., the problem is inapproximable). By integrating tools from computational complexity theory, combinatorial optimization, and social learning modeling, the work rigorously characterizes the intrinsic computational hardness of maximizing truth learning. It thereby establishes fundamental theoretical limits on network information design and learning mechanism efficacy, providing a foundational characterization of the solvability boundary for distributed learning systems.

Technology Category

• Search and Optimization: Learning to Search
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Sequential learning models situations where agents predict a ground truth in sequence, by using their private, noisy measurements, and the predictions of agents who came earlier in the sequence. We study sequential learning in a social network, where agents only see the actions of the previous agents in their own neighborhood. The fraction of agents who predict the ground truth correctly depends heavily on both the network topology and the ordering in which the predictions are made. A natural question is to find an ordering, with a given network, to maximize the (expected) number of agents who predict the ground truth correctly. In this paper, we show that it is in fact NP-hard to answer this question for a general network, with both the Bayesian learning model and a simple majority rule model. Finally, we show that even approximating the answer is hard.

Problem

• Sequential learning in social networks
• Maximizing correct truth predictions
• NP-hardness in network ordering

Innovation

• Sequential learning models
• Social network topology
• NP-hard optimization problem