Non-Bayesian Social Learning with Uncertain Models over Time-Varying Directed Graphs

TL;DR

This paper introduces a new algorithm for non-Bayesian social learning that effectively handles uncertain models and time-varying directed networks, improving hypothesis identification accuracy from finite observational data.

Contribution

It proposes a novel iterative belief construction algorithm suitable for dynamic directed graphs with non-doubly stochastic weights, addressing limitations of existing methods.

Findings

Existing methods may incorrectly select hypotheses with non-zero probability.

The new algorithm accurately supports hypotheses based on empirical evidence.

It is applicable to networks with time-varying directed connections.

Abstract

We study the problem of non-Bayesian social learning with uncertain models, in which a network of agents seek to cooperatively identify the state of the world based on a sequence of observed signals. In contrast with the existing literature, we focus our attention on the scenario where the statistical models held by the agents about possible states of the world are built from finite observations. We show that existing non-Bayesian social learning approaches may select a wrong hypothesis with non-zero probability under these conditions. Therefore, we propose a new algorithm to iteratively construct a set of beliefs that indicate whether a certain hypothesis is supported by the empirical evidence. This new algorithm can be implemented over time-varying directed graphs, with non{-}doubly stochastic weights.