A technique for certified machine unlearning that applies controlled random perturbations to gradient computations during the unlearning update, as proposed in ZHANGZ2022. Rather than computing the exact gradient of the loss with respect to the model parameters, the method evaluates gradients under random perturbations, producing a smoothed gradient function with reduced sensitivity to any individual training data point.
The approach draws on the broader randomized smoothing paradigm from certified robustness, where a function f(x) is replaced by its smoothed counterpart E[f(x + noise)]. Applied to the unlearning gradient, this smoothing inherently limits the influence that removing a single data point can have on the gradient computation. The reduced sensitivity directly translates to tighter (epsilon, delta)-certification budgets for the unlearning mechanism.
This approach offers a computational advantage over Hessian-based certified unlearning methods (such as those in ZHANGB2024) by avoiding the expensive inverse Hessian computation entirely. When combined with model quantization for unlearning, the sensitivity is further reduced by discretizing the parameter space, enabling tighter certification guarantees.