From Adaptive Query Release to Machine Unlearning

We formalize the problem of machine unlearning as design of efficient unlearning algorithms corresponding to learning algorithms which perform a selection of adaptive queries from structured query classes. We give efficient unlearning algorithms for linear and prefix-sum query classes. As applications, we show that unlearning in many problems, in particular, stochastic convex optimization (SCO), can be reduced to the above, yielding improved guarantees for the problem. In particular, for smooth Lipschitz losses and any ρ>0, our results yield an unlearning algorithm with excess population risk of tilde Obig(frac1√n+frac√dnρbig) with unlearning query (gradient) complexity tilde O(ρ · Retraining Complexity), where d is the model dimensionality and n is the initial number of samples. For non-smooth Lipschitz losses, we give an unlearning algorithm with excess population risk tilde Obig(frac1√n+big(frac√dnρbig)1/2big) with the same unlearning query (gradient) complexity. Furthermore, in the special case of Generalized Linear Models (GLMs), such as those in linear and logistic regression, we get dimension-independent rates of tilde Obig(frac1√n +frac1(nρ)2/3big) and tilde Obig(frac1√n +frac1(nρ)1/3big) for smooth Lipschitz and non-smooth Lipschitz losses respectively. Finally, we give generalizations of the above from one unlearning request to textitdynamic streams consisting of insertions and deletions.