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# Ticketed Learning–Unlearning Schemes

*Proceedings of Thirty Sixth Conference on Learning Theory*, PMLR 195:5110-5139, 2023.

#### Abstract

We consider the learning–unlearning paradigm defined as follows. First given a dataset, the goal is to learn a good predictor, such as one minimizing a certain loss. Subsequently, given any subset of examples that wish to be unlearnt, the goal is to learn, without the knowledge of the original training dataset, a good predictor that is identical to the predictor that would have been produced when learning from scratch on the surviving examples.We propose a new ticketed model for learning–unlearning wherein the learning algorithm can send back additional information in the form of a small-sized (encrypted) “ticket” to each participating training example, in addition to retaining a small amount of “central” information for later. Subsequently, the examples that wish to be unlearnt present their tickets to the unlearning algorithm, which additionally uses the central information to return a new predictor. We provide space-efficient ticketed learning–unlearning schemes for a broad family of concept classes, including thresholds, parities, intersection-closed classes, among others.En route, we introduce the count-to-zero problem, where during unlearning, the goal is to simply know if there are any examples that survived. We give a ticketed learning–unlearning scheme for this problem that relies on the construction of Sperner families with certain properties, which might be of independent interest.