Adaptive Polling in Hierarchical Social Networks using Blackwell Dominance

TL;DR

This paper develops adaptive polling strategies for hierarchical social networks modeled as POMDPs, using Blackwell dominance to create efficient policies that minimize polling costs while accounting for the evolving state and influence structure.

Contribution

It introduces novel Blackwell dominance conditions for adaptive polling in hierarchical networks, enabling the design of near-optimal policies with provable bounds.

Findings

Blackwell dominance conditions enable efficient policy design.

Adaptive polling reduces costs compared to non-adaptive methods.

Numerical results demonstrate effectiveness with real YouTube data.

Abstract

Consider a population of individuals that observe an underlying state of nature that evolves over time. The population is classified into different levels depending on the hierarchical influence that dictates how the individuals at each level form an opinion on the state. The population is sampled sequentially by a pollster and the nodes (or individuals) respond to the questions asked by the pollster. This paper considers the following problem: How should the pollster poll the hierarchical social network to estimate the state while minimizing the polling cost (measurement cost and uncertainty in the Bayesian state estimate)? This paper proposes adaptive versions of the following polling methods: Intent Polling, Expectation Polling, and the recently proposed Neighbourhood Expectation Polling to account for the time varying state of nature and the hierarchical influence in social networks. The adaptive polling problem in a hierarchical social network is formulated as a partially observed Markov decision process (POMDP). Our main results exploit the structure of the polling problem, and determine novel conditions for Blackwell dominance to construct myopic policies that provably upper bound the optimal policy of the adaptive polling POMDP. The LeCam deficiency is used to determine approximate Blackwell dominance for general polling problems. These Blackwell dominance conditions also facilitate the comparison of Renyi Divergence and Shannon capacity of more general channel structures that arise in hierarchical social networks. Numerical examples are provided to illustrate the adaptive polling policies with parameters estimated from YouTube data.