PVF-FD: Free-Rider Detection in Privacy-Preserving Vertical Federated Learning

Vertical federated learning (VFL) enables collaborative learning across different entities with disjoint data features for the same instances. In VFL, passive parties with partial data features extract embeddings from their data and forward them to the active party, which holds disjoint data features and labels, for aggregation and subsequent prediction. However, some passive parties may act as free-riders and submit valueless embeddings to deceive rewards, which undermines the fairness of collaborative training and increases communication overhead. Compared to horizontal federated learning (HFL), detecting free-riders in VFL is more challenging due to the distinct data features and heterogeneous embeddings each party produces. This makes it difficult to identify disguised embeddings of free-riders using anomaly detection methods typically employed in HFL. This paper proposes the first free-rider detection strategy in VFL using an unsupervised auxiliary task based on maximum mean discrepancy (MMD). It helps benign parties capture shared information from the active party, resulting in smaller MMD distances for benign embeddings compared to those of free-riders. Additionally, considering that embeddings may be exploited to infer local data, we introduce PVF-FD, a ciphertext-domain verifiable embedding learning scheme that enables the main and auxiliary tasks to be performed simultaneously in a privacy-preserving manner. We formally analyze the security of PVF-FD. Experimental results demonstrate that PVF-FD can effectively detect free-riders, reduce communication overhead, and maintain the performance of the main task.