Efficient machine unlearning with minimax optimality

TL;DR

This paper introduces a minimax optimal statistical framework for machine unlearning, enabling efficient data removal with theoretical guarantees and minimal data access.

Contribution

It develops a new unlearning method with minimax optimality for squared loss and provides asymptotically valid inference without full retraining.

Findings

ULS achieves near-retraining performance with less data access

The estimation error decomposes into oracle and unlearning costs

The method is validated through numerical experiments and real-data applications

Abstract

There is a growing demand for efficient data removal to comply with regulations like the GDPR and to mitigate the influence of biased or corrupted data. This has motivated the field of machine unlearning, which aims to eliminate the influence of specific data subsets without the cost of full retraining. In this work, we propose a statistical framework for machine unlearning with generic loss functions and establish theoretical guarantees. For squared loss, especially, we develop Unlearning Least Squares (ULS) and establish its minimax optimality for estimating the model parameter of remaining data when only the pre-trained estimator, forget samples, and a small subsample of the remaining data are available. Our results reveal that the estimation error decomposes into an oracle term and an unlearning cost determined by the forget proportion and the forget model bias. We further establish asymptotically valid inference procedures without requiring full retraining. Numerical experiments and real-data applications demonstrate that the proposed method achieves performance close to retraining while requiring substantially less data access.