Unlearning with Asymmetric Sources: Improved Unlearning-Utility Trade-off with Public Data

TL;DR

This paper introduces Asymmetric Langevin Unlearning (ALU), a novel framework that uses public data to improve the efficiency and utility of machine unlearning, especially under distribution mismatch.

Contribution

The paper proposes ALU, which leverages public data to reduce unlearning costs and maintain utility, providing theoretical guarantees and empirical validation.

Findings

Public data injection suppresses unlearning cost by O(1/n_pub^2).

ALU enables mass unlearning of constant dataset fractions.

ALU effectively thwarts privacy attacks while preserving utility under distribution shifts.

Abstract

Noise-based certified machine unlearning currently faces a hard ceiling: the noise magnitude required to certify unlearning typically destroys model utility, particularly for large-scale deletion requests. While leveraging public data is a standard technique in differential privacy to relax this tension, its role in unlearning remains unexplored. We address this gap by introducing Asymmetric Langevin Unlearning (ALU), a framework that uses public data to mitigate privacy costs. We prove that public data injection suppresses the unlearning cost by a factor of $O(1/n_{\mathrm{pub}}^2)$, guaranteeing a strict computational advantage over retraining. This establishes a new control mechanism: practitioners can mitigate the need for high noise-and the associated utility loss-by increasing the volume of public data. Crucially, we analyze the realistic setting of distribution mismatch, explicitly characterizing how shifts between public and private sources impact utility. We show that ALU enables mass unlearning of constant dataset fractions -- a regime where standard symmetric methods become impractical -- while maintaining high utility. Empirical evaluations using variational R\'enyi divergence and membership inference attacks confirm that ALU effectively thwarts privacy attacks while preserving utility under reasonable distribution shifts.