Distributed Social Learning With Imperfect Information

We consider the social learning problem in the paper, where the individuals in a social group need to choose one of the given options with unknown stochastic qualities to gain payoffs. This problem has been attracting increasing attention in recent years, but most of the existing proposals entail perfect information to ensure the learning efficacy, while collecting information globally to support highly efficient learning entails considerable overhead in general social networks. In this paper, we propose an iterative three-staged algorithm consisting of sampling, selection and adoption in each iteration. In particular, in a general multi-hop social network (possibly with malicious nodes), we innovate in fully exploiting the imperfect information over the social network to achieve a nearly optimal regret with light-weight communication and time complexities. We also perform solid theoretic analysis and extensive simulations to verify the efficacy of our proposed algorithm.