Partial Information Sharing over Social Learning Networks

TL;DR

This paper investigates how social learning networks can effectively share partial information about hypotheses, analyzing conditions for successful truth learning and potential vulnerabilities to deception.

Contribution

It introduces methods for partial belief sharing in social learning, extending traditional models that share full beliefs, and analyzes their impact on learning outcomes.

Findings

Partial sharing can still lead to correct hypothesis identification under certain conditions.

Different learning regimes emerge depending on sharing strategies and problem characteristics.

Networks can be deceived if the hypothesis of interest is close to the true hypothesis.

Abstract

This work addresses the problem of sharing partial information within social learning strategies. In traditional social learning, agents solve a distributed multiple hypothesis testing problem by performing two operations at each instant: first, agents incorporate information from private observations to form their beliefs over a set of hypotheses; second, agents combine the entirety of their beliefs locally among neighbors. Within a sufficiently informative environment and as long as the connectivity of the network allows information to diffuse across agents, these algorithms enable agents to learn the true hypothesis. Instead of sharing the entirety of their beliefs, this work considers the case in which agents will only share their beliefs regarding one hypothesis of interest, with the purpose of evaluating its validity, and draws conditions under which this policy does not affect truth learning. We propose two approaches for sharing partial information, depending on whether agents behave in a self-aware manner or not. The results show how different learning regimes arise, depending on the approach employed and on the inherent characteristics of the inference problem. Furthermore, the analysis interestingly points to the possibility of deceiving the network, as long as the evaluated hypothesis of interest is close enough to the truth.