Over the past years, Machine Learning-as-a-Service (MLaaS) has received a surging demand for supporting Machine Learning-driven services to offer revolutionized user experience across diverse application areas. MLaaS provides inference service with low inference latency based on an ML model trained using a dataset collected from numerous individual data owners. Recently, for the sake of data owners' privacy and to comply with the "right to be forgotten (RTBF)" as enacted by data protection legislation, many machine unlearning methods have been proposed to remove data owners' data from trained models upon their unlearning requests. However, despite their promising efficiency, almost all existing machine unlearning methods handle unlearning requests independently from inference requests, which unfortunately introduces a new security issue of inference service obsolescence and a privacy vulnerability of undesirable exposure for machine unlearning in MLaaS.

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.