Byzantine-robust decentralized stochastic optimization over static and time-varying networks

In this paper, we consider the Byzantine-robust stochastic optimization problem defined over decentralized static and time-varying networks, where agents collaboratively minimize summation of expectations local cost functions, but some are unreliable due to data corruptions, equipment failures or cyber-attacks. The agents, which called as Byzantine thereafter, can send faulty values their neighbors bias process. Our key idea handle attacks is formulate a total variation (TV) norm-penalized approximation Byzantine-free problem, penalty term forces models regular be close, also allows existence outliers from agents. A subgradient method applied solve penalized problem. We prove that proposed reaches neighborhood optimal solution, size determined by number network topology. Numerical experiments corroborate theoretical analysis, well demonstrate robustness its superior performance comparing existing methods.