We study the problem of unlearning datapoints from a learnt model. The learner first receives a dataset $S$ drawn i.i.d. from an unknown distribution, and outputs a model $widehat{w}$ that performs well on unseen samples from the same distribution. However, at some point in the future, any training datapoint $z in S$ can request to be unlearned, thus prompting the learner to modify its output model while still ensuring the same accuracy guarantees. We initiate a rigorous study of generalization in machine unlearning, where the goal is to perform well on previously unseen datapoints. Our focus is on both computational and storage complexity. For the setting of convex losses, we provide an unlearning algorithm that can unlearn up to $O(n/d^{1/4})$ samples, where $d$ is the problem dimension. In comparison, in general, differentially private learning (which implies unlearning) only guarantees deletion of $O(n/d^{1/2})$ samples. This demonstrates a novel separation between differential privacy and machine unlearning.
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