PDF: Path-Dependent Client Selection for Federated Unlearning

Federated unlearning (FU) aims to remove target clients' influence from a trained model without full retraining. Existing methods largely treat unlearning as a post-hoc operation, overlooking that client influence is path-dependent: contributions made during critical learning periods (CLPs) can have disproportionate and persistent effects. Moreover, involving all retained clients is costly and impractical because clients differ in their usefulness for unlearning and may be intermittently available. We introduce PDF, a path-dependent client-selection framework that maintains lightweight, target-agnostic, CLP-weighted histories of each client's update direction and global-model alignment. Upon an unlearning request, PDF combines historical global alignment with target decoupling to select top-$k$ retained clients for retraining-based unlearning. Theoretically, we characterize the propagation of client perturbations, derive sufficient conditions for one-step retained-loss reduction and target-loss increase, and bound the initialization selection-utility gap assuming consistency between path-dependence scores and first-order client utility. Experiments on FMNIST, CIFAR-10, and CIFAR-100 under varying data heterogeneity in a label-flipping client-removal setting show that PDF achieves effective forgetting and strong retained utility using only approximately $40$% of the retained clients. On non-IID CIFAR-10, PDF achieves $0$% forgetting accuracy with an MIA AUC within $0.88$ percentage points of Retrain. On CIFAR-100, it improves retained accuracy by up to $6.91$ percentage points over the strongest evaluated FU baselines. Across evaluated scenarios, PDF reduces communication by approximately $69$% and computation by $57$-$61$% relative to Retrain.