首个可理论保证的垂直联邦学习遗忘框架，支持任意数据随时删除。

Privacy concerns in machine learning are heightened by regulations such as the GDPR, which enforces the "right to be forgotten" (RTBF), driving the emergence of machine unlearning as a critical research field. Vertical Federated Learning (VFL) enables collaborative model training by aggregating a sample's features across distributed parties while preserving data privacy at each source. This paradigm has seen widespread adoption in healthcare, finance, and other privacy-sensitive domains. However, existing VFL systems lack robust mechanisms to comply with RTBF requirements, as unlearning methodologies for VFL remain underexplored. In this work, we introduce the first VFL framework with theoretically guaranteed unlearning capabilities, enabling the removal of any data at any time. Unlike prior approaches -- which impose restrictive assumptions on model architectures or data types for removal -- our solution is model- and data-agnostic, offering universal compatibility. Moreover, our framework supports asynchronous unlearning, eliminating the need for all parties to be simultaneously online during the forgetting process. These advancements address critical gaps in current VFL systems, ensuring compliance with RTBF while maintaining operational flexibility.We make all our implementations publicly available at https://github.com/wangln19/vertical-federated-unlearning.