Descent-to-Delete: Gradient-Based Methods for Machine Unlearning

TL;DR

This paper introduces gradient-based algorithms for machine unlearning in convex models, capable of handling long adversarial update sequences with stable error and runtime, and explores different statistical indistinguishability criteria.

Contribution

It presents the first data deletion algorithms for convex models that maintain efficiency over long adversarial update sequences and introduces new conceptual distinctions in unlearning.

Findings

Algorithms handle arbitrarily long adversarial updates.

Steady-state error and runtime do not grow with update sequence length.

More efficient algorithms are developed under weaker indistinguishability conditions.

Abstract

We study the data deletion problem for convex models. By leveraging techniques from convex optimization and reservoir sampling, we give the first data deletion algorithms that are able to handle an arbitrarily long sequence of adversarial updates while promising both per-deletion run-time and steady-state error that do not grow with the length of the update sequence. We also introduce several new conceptual distinctions: for example, we can ask that after a deletion, the entire state maintained by the optimization algorithm is statistically indistinguishable from the state that would have resulted had we retrained, or we can ask for the weaker condition that only the observable output is statistically indistinguishable from the observable output that would have resulted from retraining. We are able to give more efficient deletion algorithms under this weaker deletion criterion.