Decentralized Byzantine-Resilient Stochastic Optimization Over Multi-Agent Systems with Arbitrary Communication Delays

Byzantine failures and communication delays impose great challenges to the decision-making process of multiagent systems (MASs). In this paper, we aim to resolve a category of general finite-sum optimization problems with simultaneous presence of Byzantine agents and arbitrary time-varying communication delays over networks. The number of Byzantine agents and their identities are unknown to reliable agents and the communication delays are not necessarily bounded. To alleviate the negative impact incurred by Byzantine agents and communication delays, both a generalized norm-penalized approximation technique and an age tracker are considered in the development of a decentralized Byzantine-resilient stochastic sub-gradient algorithm, dubbed DeSSO-AD. Theoretical analysis characterizes an explicit sub-linear convergence rate for DeSSO-AD based on a diminishing step-size. The effectiveness and resilience of DeSSO-AD are demonstrated via handling a machine-learning problem under cyber attacks and time-varying communication delays. © 2024 IEEE.