Decentralized Data-Free Unlearning in Continual Learning: Task-Conditioned Hypernetwork Approach with Theoretical Guarantee

Unlearning in decentralized continual learning requires agents to unlearn previously acquired knowledge even when the corresponding historical data are unavailable. Performing unlearning without reconstructing historical inputs presents two challenges: (1) *Lack of Direct Unlearning Supervision*, as agents lack direct supervision for unlearning the target class while preserving the remaining classes of the same task; and (2) *Cross-Task Interference during Unlearning*, as local updates and neighbor aggregation may disrupt retained tasks through shared parameters, while broadly restricting parameter changes can hinder the requested unlearning. To address these challenges, we propose Dec-UnHNet, in which a hypernetwork generates task-specific classifier heads from descriptors built with diffusion-derived class prototypes. For a data-free unlearning request, surrogate features provide supervision for unlearning the target class, while hypernetwork-output regularization anchors generated classifiers for retained tasks without historical-sample replay. Theoretically, we rigorously prove that *Dec-UnHNet* achieves an $\mathcal{O}(1/\sqrt{nQ})$ convergence rate for the decentralized joint global empirical risk across all tasks. Extensive experiments on two benchmark datasets demonstrate improved continual-learning accuracy and zero target-class accuracy at all evaluated unlearning steps.