Communication-Efficient and Fault-Tolerant Social Learning

We study the problem of decentralized non-Bayesian (social) learning with compressed communications in the presence of adversarial agents, i.e., Byzantine. The non-adversarial agents seek to collaboratively agree on a hypothesis that best describes an unknown state of the world. We propose a robust update rule where, under appropriate assumptions, non-faulty agents can reach a consensus on the true state of the world by sharing arbitrarily compressed messages over the network. We show almost sure asymptotic convergence of the beliefs of non-faulty agents around the optimal hypothesis and provide numerical evidence for the communication efficiency and robustness of the proposed algorithm.