Certified Minimax Unlearning with Generalization Rates and Deletion Capacity

TL;DR

This paper introduces a new certified unlearning algorithm for minimax models that uses a Hessian-based Newton update and Gaussian noise, providing improved generalization and deletion guarantees over existing methods.

Contribution

It develops a novel unlearning method for minimax models with theoretical guarantees, extending unlearning certification to complex models beyond standard statistical learning.

Findings

Achieves a generalization rate of O(n/d^{1/4})

Provides deletion capacity bounds maintaining population risk

Outperforms baseline differential privacy methods in rate

Abstract

We study the problem of $(\epsilon,\delta)$-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 $(\epsilon,\delta)$-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). We derive the generalization rates in terms of population strong and weak primal-dual risk for three different cases of loss functions, i.e., (strongly-)convex-(strongly-)concave losses. We also provide the deletion capacity to guarantee that a desired population risk can be maintained as long as the number of deleted samples does not exceed the derived amount. With training samples $n$ and model dimension $d$, it yields the order $\mathcal O(n/d^{1/4})$, which shows a strict gap over the baseline method of differentially private minimax learning that has $\mathcal O(n/d^{1/2})$. In addition, our rates of generalization and deletion capacity match the state-of-the-art rates derived previously for standard statistical learning models.