Robust Sequential Learning in Random Order Networks

Abstract

In the sequential learning problem, agents in a network attempt to predict a binary ground truth, informed by both a noisy private signal and the predictions of neighboring agents before them. It is well known that social learning in this setting can be highly fragile: small changes to the action ordering, network topology, or even the strength of the agents' private signals can prevent a network from converging to the truth. We study networks that achieve random-order asymptotic truth learning, in which almost all agents learn the ground truth when the decision ordering is selected uniformly at random. We analyze the robustness of these networks, showing that those achieving random-order asymptotic truth learning are resilient to a bounded number of adversarial modifications. We characterize necessary conditions for such networks to succeed in this setting and introduce several graph constructions that learn through different mechanisms. Finally, we present a randomized polynomial-time algorithm that transforms an arbitrary network into one achieving random-order learning using minimal edge or vertex modifications, with provable approximation guarantees. Our results reveal structural properties of networks that achieve random-order learning and provide algorithmic tools for designing robust social networks.