Byzantine-robust distributed vertical learning over time-varying networks

This paper focuses on Byzantine-robust distributed vertical learning problem over time-varying networks. The coupled vertical learning primal problem is transformed into a dual problem with separable cost functions based on Fenchel duality theory, and an l₁-regularization term is introduced to enhance the robustness of the optimization algorithm against Byzantine nodes. By the robust stochastic aggregation and the proximal gradient descent method, we propose a novel Byzantine-robust distributed vertical learning algorithm, and prove the equivalence between the fixed points of the proposed algorithm and the optimal solution of the dual problem. Furthermore, we provide the upper bound of convergence error for the proposed algorithm under both constant and diminishing step sizes, respectively. The effectiveness of the algorithm is also validated through numerical simulations.