Abstract: To addresses the issue of vertically partitioned data samples in distributed machine learning, the paper proposes a Byzantine-robust distributed vertical learning algorithm in adversarial environments. First, the original problem of coupled distributed vertical learning is transformed into a separable dual problem based on Fenchel duality theory, and a distributed vertical learning algorithm is then proposed using robust stochastic aggregation techniques. Then, the equivalence between the fixed point of the proposed algorithm and the optimal solution of the dual problem is proven by selecting an appropriate penalty coefficient. Finally, numerical simulations validate the superiority of the proposed algorithm.