DPZV: Elevating the Tradeoff between Privacy and Utility in Zeroth-Order Vertical Federated Learning

Abstract: Vertical Federated Learning (VFL) enables collaborative training with feature-partitioned data, yet remains vulnerable to privacy leakage through gradient transmissions. Standard differential privacy (DP) techniques such as DP-SGD are difficult to apply in this setting due to VFL's distributed nature and the high variance incurred by vector-valued noise. On the other hand, zeroth-order (ZO) optimization techniques can avoid explicit gradient exposure but lack formal privacy guarantees. In this work, we propose DPZV, the first ZO optimization framework for VFL that achieves tunable DP with performance guarantees. DPZV overcomes these limitations by injecting low-variance scalar noise at the server, enabling controllable privacy with reduced memory overhead. We conduct a comprehensive theoretical analysis showing that DPZV matches the convergence rate of first-order optimization methods while satisfying formal ($\epsilon, \delta$)-DP guarantees. Experiments on image and language benchmarks demonstrate that DPZV outperforms several baselines in terms of accuracy under a wide range of privacy constraints ($\epsilon \le 10$), thereby elevating the privacy-utility tradeoff in VFL.