Distributed Learning over Time-Varying Graphs with Adversarial Agents

In this work, we study the problem of non-Bayesian learning in time-varying (dynamic) networks when there are some adversarial (faulty) agents in the network. The set of faulty agents is fixed across time. The connectivity graph of the network is changing at each time step and is unknown to the agents. In every time step, each non-faulty agent collects partial information about an unknown state of the environment. Each non-faulty agent tries to estimate the true state of the environment by iteratively sharing information with its neighbors at each time step. We first present an analysis of a distributed algorithm in static communication network with faulty agents which does not require the network to achieve consensus. Existing algorithms in this setting require that all non-faulty agents in the network should be able to achieve consensus via local information exchange. We then extend this analysis to dynamic networks with relaxed network condition. We show that if every non-faulty agent can receive enough information (via iteratively communicating with neighbors) to differentiate the true state of the world from other possible states then it can indeed learn the true state.