Protecting the Undeleted in Machine Unlearning

Privacy protection laws, such as the GDPR, grant individuals the right to request the forgetting of their personal data not only from databases but also from machine learning (ML) models trained on them. Machine unlearning has emerged as a practical means to facilitate model forgetting of data instances seen during training. Although some existing machine unlearning methods guarantee exact forgetting, they are typically costly in computational terms. On the other hand, more affordable methods do not offer forgetting guarantees and are applicable only to specific ML models. In this paper, we present efficient unlearning with privacy guarantees (EUPG), a novel machine unlearning framework that offers formal privacy guarantees to individuals whose data are being unlearned. EUPG involves pre-training ML models on data protected using privacy models, and it enables {\em efficient unlearning with the privacy guarantees offered by the privacy models in use}. Through empirical evaluation on four heterogeneous data sets protected with $k$-anonymity and $ε$-differential privacy as privacy models, our approach demonstrates utility and forgetting effectiveness comparable to those of exact unlearning methods, while significantly reducing computational and storage costs. Our code is available at https://github.com/najeebjebreel/EUPG.

Training machine learning models requires the storage of large datasets, which often contain sensitive or private data. Storing data is associated with a number of potential risks which increase over time, such as database breaches and malicious adversaries. Machine unlearning is the study of methods to efficiently remove the influence of training data subsets from previously-trained models. Existing unlearning methods typically require direct access to the "forget set" -- the data to be forgotten-and organisations must retain this data for unlearning rather than deleting it immediately upon request, increasing risks associated with the forget set. We introduce partially-blind unlearning -- utilizing auxiliary information to unlearn without explicit access to the forget set. We also propose a practical framework Reload, a partially-blind method based on gradient optimization and structured weight sparsification to operationalize partially-blind unlearning. We show that Reload efficiently unlearns, approximating models retrained from scratch, and outperforms several forget set-dependent approaches. On language models, Reload unlearns entities using <0.025% of the retain set and <7% of model weights in <8 minutes on Llama2-7B. In the corrective case, Reload achieves unlearning even when only 10% of corrupted data is identified.

Machine unlearning updates a trained model after records are deleted, aiming to match exact retraining without repeating the full training procedure. We develop Gaussian mechanisms for Newton updates under sequential deletion requests. Using Gaussian differential privacy (GDP) and its adaptive composition rule, we show that the full sequence of released models is statistically difficult to distinguish from matched exact retraining. To calibrate these mechanisms for empirical risk minimization, we derive upper bounds on the error of the Newton approximation relative to exact retraining and on how this error changes after each deletion batch. Independent Gaussian noise is calibrated using bounds on the full residual at each release, whereas Gaussian random walk noise uses smaller bounds on residual increments. These bounds yield allocations minimizing the worst-case maximum noise variance across releases under the resulting GDP certification constraints. With count-based bounds, the random walk asymptotically matches the worst-case variance of a single release at deletion cap $M$, while independent noise incurs an additional factor of order $M$. Set-based bounds can reduce the noise variances by using gradients and Hessians of the deleted records. For singleton deletion, we further show that count-based independent noise, count-based random walk noise, and set-based independent noise are minimax among fixed Gaussian covariances under their respective residual or increment bounds. With set-based bounds, allowing variances to adapt to deleted records can improve on every fixed covariance by a factor of order $(\log M)^2$ on some data sequences. The residual and noise bounds also yield parameter and predictive consistency relative to exact retraining, uniformly over deletion policies. Simulations and a credit default data analysis evaluate bounds, noise variances, and estimation errors.