PAC Learning from Distributed Data in the Presence of Malicious Nodes

When data is distributed over a network, statistical learning needs to be carried out in a fully distributed fashion. When all nodes in the network are faultless and cooperate with each other, it is understood that the objective is probably approximately correct (PAC) learnable. However, when there are malicious nodes trying to sabotage learning by injecting false information in the network, PAC learnability of the objective remains an open question. In this paper, we discuss the distributed statistical learning problem when the risk function is strictly convex. We show that the model is PAC learnable in the presence of malicious nodes by proposing and analyzing a distributed learning algorithm. Experiments in non-convex settings are also performed to further discuss the PAC learnability of non-convex statistical learning problems from distributed data.