Adaptive Polling in Hierarchical Social Networks Using Blackwell Dominance

Abstract

This paper presents adaptive polling algorithms and their analysis for social networks having a hierarchical influence structure. The adaptive polling problem on the social network is formulated as a partially observed Markov decision process (POMDP). Our main results exploit the structure of the polling problem to determine novel conditions for Blackwell dominance that arise in hierarchical social influence networks. The Blackwell dominance conditions enable the construction of myopic policies that provably upper bound the optimal policy of the POMDP for adaptive polling. Adaptive versions of intent polling and expectation polling are developed using Blackwell dominance, and they are inexpensive to implement. For polling problems not having a Blackwell dominance structure, the Le Cam deficiency is used to determine approximate Blackwell dominance; this is used to develop an adaptive version of the recently proposed Neighbourhood Expectation Polling algorithm. The proposed Blackwell dominance conditions also facilitate the comparison of Renyi divergence and Shannon capacity of more general channel structures that arise in polling hierarchical social influence networks. Numerical examples are provided to illustrate the adaptive polling policies with parameters estimated from YouTube data.