Certified Minimax Unlearning with Generalization Rates and Deletion Capacity

We study the problem of (ϵ, δ)-certified machine unlearning for minimax models. Most of the existing works focus on unlearning from standard statistical learning models that have a single variable and their unlearning steps hinge on the direct Hessian-based conventional Newton update. We develop a new (ϵ, δ)-certified machine unlearning algorithm for minimax models. It proposes a minimax unlearning step consisting of a total Hessian-based complete Newton update and the Gaussian mechanism borrowed from differential privacy. To obtain the unlearning certification, our method injects calibrated Gaussian noises by carefully analyzing the "sensitivity" of the minimax unlearning step (i.e., the closeness between the minimax unlearning variables and the retraining-from-scratch variables).