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A Reliable Cryptographic Framework for Empirical Machine Unlearning Evaluation

Yiwen Tu, Pingbang Hu, Jiaqi Ma

TL;DR

This work focuses on membership inference attack (MIA) based evaluation, one of the most common approaches for evaluating unlearning algorithms, and proposes a practical and efficient approximation of the induced evaluation metric that measures the data removal efficacy of unlearning algorithms.

Abstract

Machine unlearning updates machine learning models to remove information from specific training samples, complying with data protection regulations that allow individuals to request the removal of their personal data. Despite the recent development of numerous unlearning algorithms, reliable evaluation of these algorithms remains an open research question. In this work, we focus on membership inference attack (MIA) based evaluation, one of the most common approaches for evaluating unlearning algorithms, and address various pitfalls of existing evaluation metrics lacking theoretical understanding and reliability. Specifically, by modeling the proposed evaluation process as a \emph{cryptographic game} between unlearning algorithms and MIA adversaries, the naturally induced evaluation metric measures the data removal efficacy of unlearning algorithms and enjoys provable guarantees that existing evaluation metrics fail to satisfy. Furthermore, we propose a practical and efficient approximation of the induced evaluation metric and demonstrate its effectiveness through both theoretical analysis and empirical experiments. Overall, this work presents a novel and reliable approach to empirically evaluating unlearning algorithms, paving the way for the development of more effective unlearning techniques.

A Reliable Cryptographic Framework for Empirical Machine Unlearning Evaluation

TL;DR

This work focuses on membership inference attack (MIA) based evaluation, one of the most common approaches for evaluating unlearning algorithms, and proposes a practical and efficient approximation of the induced evaluation metric that measures the data removal efficacy of unlearning algorithms.

Abstract

Machine unlearning updates machine learning models to remove information from specific training samples, complying with data protection regulations that allow individuals to request the removal of their personal data. Despite the recent development of numerous unlearning algorithms, reliable evaluation of these algorithms remains an open research question. In this work, we focus on membership inference attack (MIA) based evaluation, one of the most common approaches for evaluating unlearning algorithms, and address various pitfalls of existing evaluation metrics lacking theoretical understanding and reliability. Specifically, by modeling the proposed evaluation process as a \emph{cryptographic game} between unlearning algorithms and MIA adversaries, the naturally induced evaluation metric measures the data removal efficacy of unlearning algorithms and enjoys provable guarantees that existing evaluation metrics fail to satisfy. Furthermore, we propose a practical and efficient approximation of the induced evaluation metric and demonstrate its effectiveness through both theoretical analysis and empirical experiments. Overall, this work presents a novel and reliable approach to empirically evaluating unlearning algorithms, paving the way for the development of more effective unlearning techniques.
Paper Structure (51 sections, 7 theorems, 36 equations, 1 figure, 8 tables, 1 algorithm)

This paper contains 51 sections, 7 theorems, 36 equations, 1 figure, 8 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Machine unlearning
  4. Machine unlearning evaluation
  5. Proposed evaluation framework
  6. Preliminaries
  7. Unlearning sample inference game
  8. Initialization.
  9. Challenger Phase.
  10. Adversary Phase.
  11. Advantage and unlearning quality
  12. Zero Grounding for $\mathop{\mathrm{\normalfont\textsc{Retrain}}}\nolimits$.
  13. Guarantee Under Certified Removal.
  14. SWAP test
  15. SWAP Test versus Random Splits.
  16. ...and 36 more sections

Key Result

Theorem 3.1

For any adversary $\mathcal{A}$, $\mathop{\mathrm{Adv}}\nolimits(\mathcal{A}, \mathop{\mathrm{\normalfont\textsc{Retrain}}}\nolimits) = 0$ where $\mathop{\mathrm{\normalfont\textsc{Retrain}}}\nolimits$ is the retraining method. Hence, $\mathcal{Q}(\mathop{\mathrm{\normalfont\textsc{Retrain}}}\nolimi

Figures (1)

  • Figure 1: The unlearning sample inference game framework for our machine unlearning evaluation.

Theorems & Definitions (21)

  • Definition 1: Advantage
  • Definition 2: Unlearning Quality
  • Theorem 3.1: Zero Grounding
  • Definition 3: Certified Removal guo2020certified; Informal
  • Theorem 3.2: Guarantee Under Certified Removal
  • Proposition 1: Zero Grounding of SWAP Test (Informal)
  • Proposition 2: High Advantage Under Random Splits
  • Remark 1: Offsetting MIA Accuracy/AUC for $\mathop{\mathrm{\normalfont\textsc{Retrain}}}\nolimits$
  • Remark 2
  • Remark 3
  • ...and 11 more