Byzantine-resilient federated online learning for Gaussian process regression

In this paper, we study Byzantine-resilient federated online learning for Gaussian process regression (GPR). We develop a Byzantine-resilient federated GPR algorithm that allows a cloud and a group of agents to collaboratively learn a latent function and improve the learning performances where some agents exhibit Byzantine failures, i.e., arbitrary and potentially adversarial behavior. Each agent-based local GPR sends potentially compromised local predictions to the cloud, and the cloud-based aggregated GPR computes a global model by a Byzantine-resilient product of experts aggregation rule. Then the cloud broadcasts the current global model to all the agents. Agent-based fused GPR refines local predictions by fusing the received global model with that of the agent-based local GPR. Moreover, we quantify the learning accuracy improvements of the agent-based fused GPR over the agent-based local GPR. Experiments on a toy example and two medium-scale real-world datasets are conducted to demonstrate the performances of the proposed algorithm.