When to Forget? Complexity Trade-offs in Machine Unlearning

TL;DR

This paper investigates the computational complexity of machine unlearning, establishing bounds and phase regimes that determine when unlearning is feasible, trivial, or advantageous over retraining, based on data and privacy factors.

Contribution

It provides the first theoretical bounds and a phase diagram for unlearning complexity, revealing regimes where unlearning is computationally feasible or trivial.

Findings

Identifies three regimes of unlearning complexity: infeasible, trivial, and advantageous.

Establishes upper and lower bounds on minimax computation times for unlearning.

Highlights the impact of data dimensionality, sample size, and privacy on unlearning feasibility.

Abstract

Machine Unlearning (MU) aims at removing the influence of specific data points from a trained model, striving to achieve this at a fraction of the cost of full model retraining. In this paper, we analyze the efficiency of unlearning methods and establish the first upper and lower bounds on minimax computation times for this problem, characterizing the performance of the most efficient algorithm against the most difficult objective function. Specifically, for strongly convex objective functions and under the assumption that the forget data is inaccessible to the unlearning method, we provide a phase diagram for the unlearning complexity ratio -- a novel metric that compares the computational cost of the best unlearning method to full model retraining. The phase diagram reveals three distinct regimes: one where unlearning at a reduced cost is infeasible, another where unlearning is trivial because adding noise suffices, and a third where unlearning achieves significant computational advantages over retraining. These findings highlight the critical role of factors such as data dimensionality, the number of samples to forget, and privacy constraints in determining the practical feasibility of unlearning.