Machine Unlearning under an Uncertain Forget Set via Distributional Optimization

Machine unlearning, which aims to remove the influence of specific training samples, has received increasing attention as demands grow to remove harmful or unwanted data. Existing unlearning methods typically assume that the forget set is known exactly. However, this assumption is often impractical when detectors provide uncertain sample-wise evidence rather than a verified forget set. Under such uncertainty, prior methods reduce this evidence to retain-or-forget decisions and discard how strongly each sample should be forgotten. To address this, we propose Uncertainty-Aware Distributional Unlearning (UADU), which directly operates on continuous forgetting likelihoods. UADU (i) introduces a Likelihood-Conditioned Unlearning Objective (LCUO) that combines the training label probabilities of retain and reference-based forget targets according to forgetting likelihoods, and (ii) develops Entropy-Constrained Distributional Optimization (ECDO) to preserve the LCUO-specified training label probability and redistribute the remaining probability mass under an entropy criterion. We further provide theoretical guarantees for target approximation and local redistribution optimality. Extensive experiments on three benchmark datasets demonstrate the effectiveness and efficiency of UADU under uncertain forget sets.