We present HDP-VFL, the first hybrid differentially private (DP) framework for vertical federated learning (VFL) to demonstrate that it is possible to jointly learn a generalized linear model (GLM) from vertically partitioned data with only a negligible cost, w.r.t. training time, accuracy, etc., comparing to idealized non-private VFL. Our work builds on the recent advances in VFL-based collaborative training among different organizations which rely on protocols like Homomorphic Encryption (HE) and Secure Multi-Party Computation (MPC) to secure computation and training. In particular, we analyze how VFLs intermediate result (IR) can leak private information of the training data during communication and design a DP-based privacy-preserving algorithm to ensure the data confidentiality of VFL participants. We mathematically prove that our algorithm not only provides utility guarantees for VFL, but also offers multi-level privacy, i.e. DP w.r.t. IR and joint differential privacy (JDP) w.r.t. model weights. Experimental results demonstrate that our work, under adequate privacy budgets, is quantitatively and qualitatively similar to GLMs, learned in idealized non-private VFL setting, rather than the increased cost in memory and processing time in most prior works based on HE or MPC. Our codes will be released if this paper is accepted.
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