Less Noise, Same Certificate: Retain Sensitivity for Unlearning

TL;DR

This paper introduces retain sensitivity, a new approach that reduces noise in certified machine unlearning by focusing only on data deletions, leading to more accurate unlearning with less added noise.

Contribution

The paper proposes retain sensitivity, a concept that allows for less noise in certified unlearning by not protecting retained data, improving utility over traditional DP-based methods.

Findings

Retain sensitivity reduces noise compared to DP-based calibration.

Validated reductions in noise across PCA, MST, and ERM problems.

Refined unlearning algorithms with improved utility using retain sensitivity.

Abstract

Certified machine unlearning aims to provably remove the influence of a deletion set $U$ from a model trained on a dataset $S$, by producing an unlearned output that is statistically indistinguishable from retraining on the retain set $R:=S\setminus U$. Many existing certified unlearning methods adapt techniques from Differential Privacy (DP) and add noise calibrated to global sensitivity, i.e., the worst-case output change over all adjacent datasets. We show that this DP-style calibration is often overly conservative for unlearning, based on a key observation: certified unlearning, by definition, does not require protecting the privacy of the retained data $R$. Motivated by this distinction, we define retain sensitivity as the worst-case output change over deletions $U$ while keeping $R$ fixed. While insufficient for DP, retain sensitivity is exactly sufficient for unlearning, allowing for the same certificates with less noise. We validate these reductions in noise theoretically and empirically across several problems, including the weight of minimum spanning trees, PCA, and ERM. Finally, we refine the analysis of two widely used certified unlearning algorithms through the lens of retain sensitivity, leveraging the regularity induced by $R$ to further reduce noise and improve utility.