A Byzantine-resilient Dual Subgradient Method for Vertical Federated Learning

Federated learning (FL) raises new challenges on security risks especially when Byzantine clients exist to send corrupted or adversarial messages to deteriorate the training paradigm. While there is an extensive research on robust algorithms for horizontal or data-partitioned FL problems, the exploration in Byzantine-resilient vertical or feature-partitioned FL is quite limited. In this paper, we provide a problem formulation of vertical FL in the presence of Byzantine attacks, and propose a Byzantine-resilient dual subgradient method. Convergence analysis is established for the proposed algorithm, and the influence of the Byzantine clients is also clarified. Numerical experiments show the proposed algorithm is robust to various Byzantine attacks to vertical FL.