PIGR-VFL: Partition-Induced-Gap Reduction Vertical Federated Learning

Vertical Federated Learning (VFL) enables $K$ clients to collaboratively exploit partitioned feature blocks without sharing their raw features. However, when each client holds an increasingly fine-grained partitioned feature block, aggregating local representations obtained by local extraction models may cause information loss and degrade predictive performance. To address this issue, we first derive a worst-case bound on the population risk to identify the factors responsible for this VFL-specific partition-induced performance degradation. Decomposing this bound suggests that combining model architectural designs (coordinate-preserving embedding, participant-mean aggregation) with optional training objectives (extraction-curvature regularization, proximal extraction-output regularization) reduces the identified factors without unduly restricting the extraction model's expressiveness; we refer to the resulting method as Partition-Induced-Gap Reduction VFL (PIGR-VFL). Through numerical experiments, we confirm the effectiveness of PIGR-VFL, particularly on image classification tasks.