提出随机梯度下降的删数据算法，理论保证删除效果。

Machine unlearning algorithms aim to remove the impact of selected training data from a model without the computational expenses of retraining from scratch. Two such algorithms are ``Descent-to-Delete" (D2D) and ``Rewind-to-Delete" (R2D), full-batch gradient descent algorithms that are easy to implement and satisfy provable unlearning guarantees. In particular, the stochastic version of D2D is widely implemented as the ``finetuning" unlearning baseline, despite lacking theoretical backing on nonconvex functions. In this work, we prove $(\varepsilon, δ)$ certified unlearning guarantees for stochastic R2D and D2D for strongly convex, convex, and nonconvex loss functions, by analyzing unlearning through the lens of disturbed or biased gradient systems, which may be contracting, semi-contracting, or expansive respectively. Our argument relies on optimally coupling the random behavior of the unlearning and retraining trajectories, resulting in a sensitivity bound that holds in expectation that yields $(\varepsilon, δ)$ unlearning. We determine that D2D can yield tighter guarantees for strongly convex functions, but R2D is more appropriate for convex and nonconvex functions. Finally, we compare the algorithms empirically, demonstrating the strengths and weaknesses of each approach.