Byzantine-robust Distributed Stochastic Non-convex Optimization in Adversarial Environments over Unbalanced Networks

This paper focuses on a Byzantine-robust distributed stochastic non-convex optimization problem with smooth local cost functions over unbalanced networks. In particular, the nodes in a network are to find a stationary solution minimizing a sum of smooth cost functions, while some of unreliable or malicious Byzantine nodes can spread faulty values in the network to disturb both the update of the algorithm and the computation of the weighted matrix. By using a robust clipping-based aggregation method with adaptive thresholds, we propose a novel Byzantine-robust distributed stochastic optimization algorithm over unbalanced networks. Furthermore, we prove that our proposed algorithm can converge to a neighborhood of the stationary solution, of which the size is related to the network topology and the heterogeneity between different nodes. Numerical experiment is given to demonstrate the effectiveness of the proposed algorithm against Byzantine attacks.