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A Game-Theoretic Analysis of Auditing Differentially Private Algorithms with Epistemically Disparate Herd

Ya-Ting Yang, Tao Zhang, Quanyan Zhu

TL;DR

Addresses the challenge of auditing privacy-preserving algorithms when audits are costly; this work constructs a Stackelberg herd-audit framework with a leader (developer) and heterogeneous followers (auditors) subject to rational inattention linked to $\epsilon$-DP; derives Bayes rule and optimal information strategies, and characterizes equilibria showing that lower $\lambda$ and lower information costs improve audit confidence and deter deviant behavior; concludes that herd audits can credibly threaten developers and enhance the responsible deployment of privacy preserving AI, with future work on end-user incentives and distributed-central auditing.

Abstract

Privacy-preserving AI algorithms are widely adopted in various domains, but the lack of transparency might pose accountability issues. While auditing algorithms can address this issue, machine-based audit approaches are often costly and time-consuming. Herd audit, on the other hand, offers an alternative solution by harnessing collective intelligence. Nevertheless, the presence of epistemic disparity among auditors, resulting in varying levels of expertise and access to knowledge, may impact audit performance. An effective herd audit will establish a credible accountability threat for algorithm developers, incentivizing them to uphold their claims. In this study, our objective is to develop a systematic framework that examines the impact of herd audits on algorithm developers using the Stackelberg game approach. The optimal strategy for auditors emphasizes the importance of easy access to relevant information, as it increases the auditors' confidence in the audit process. Similarly, the optimal choice for developers suggests that herd audit is viable when auditors face lower costs in acquiring knowledge. By enhancing transparency and accountability, herd audit contributes to the responsible development of privacy-preserving algorithms.

A Game-Theoretic Analysis of Auditing Differentially Private Algorithms with Epistemically Disparate Herd

TL;DR

Addresses the challenge of auditing privacy-preserving algorithms when audits are costly; this work constructs a Stackelberg herd-audit framework with a leader (developer) and heterogeneous followers (auditors) subject to rational inattention linked to -DP; derives Bayes rule and optimal information strategies, and characterizes equilibria showing that lower and lower information costs improve audit confidence and deter deviant behavior; concludes that herd audits can credibly threaten developers and enhance the responsible deployment of privacy preserving AI, with future work on end-user incentives and distributed-central auditing.

Abstract

Privacy-preserving AI algorithms are widely adopted in various domains, but the lack of transparency might pose accountability issues. While auditing algorithms can address this issue, machine-based audit approaches are often costly and time-consuming. Herd audit, on the other hand, offers an alternative solution by harnessing collective intelligence. Nevertheless, the presence of epistemic disparity among auditors, resulting in varying levels of expertise and access to knowledge, may impact audit performance. An effective herd audit will establish a credible accountability threat for algorithm developers, incentivizing them to uphold their claims. In this study, our objective is to develop a systematic framework that examines the impact of herd audits on algorithm developers using the Stackelberg game approach. The optimal strategy for auditors emphasizes the importance of easy access to relevant information, as it increases the auditors' confidence in the audit process. Similarly, the optimal choice for developers suggests that herd audit is viable when auditors face lower costs in acquiring knowledge. By enhancing transparency and accountability, herd audit contributes to the responsible development of privacy-preserving algorithms.
Paper Structure (22 sections, 4 theorems, 31 equations, 5 figures)

This paper contains 22 sections, 4 theorems, 31 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Herd Auditors with Epistemic Disparity
  3. Bayes hypothesis testing as the auditor's decision rule
  4. Auditor's choice of the information strategy
  5. Stackelberg Herd Audit Game
  6. Connection to differential privacy
  7. Problem Setting for the Developer
  8. Responsible developer
  9. Irresponsible developer
  10. Revisiting the Auditor's Problem
  11. Revisit the Irresponsible Developer's Problem
  12. Equilibrium Analysis
  13. The auditor's optimal strategy
  14. The irresponsible developer's optimal strategy
  15. Auditor's audit confidence and epistemic factor
  16. ...and 7 more sections

Key Result

Proposition 1

A responsible developer's mixed strategy reduces to a pure strategy by letting all the mass on $\epsilon = \epsilon^{\prime}$. Hence, $Q_g(s) = \sum_{\epsilon}p(s|\epsilon) q(\epsilon|g) = p(s|\epsilon^{\prime})$.

Figures (5)

  • Figure 1: A herd of diverse end-users act as auditors to inspect the AI algorithm used in the developed product.
  • Figure 2: An illustration of how the auditor performs audit. The auditor acquires information $s$ about the unknown state $\omega$ using strategy $d$ and then makes a decision $a$ using strategy $\delta$.
  • Figure 3: The Stackelberg herd audit game.
  • Figure 4: Trends between the auditor's confidence (posterior belief) and the auditor's epistemic factor ($\mu(g)=\mu(b)=0.5, u(b, T)=u(g, F)=-1$). Left: $\chi(s)<0$ ($Q_b(s)/v(s)=0.25$). Right: $-\chi(s)<0$ ($Q_b(s)/v(s)=0.85$).
  • Figure 5: The trend between the auditor's confidence and the irresponsible developer's choice that leads to $Q_b(s)/v(s)$. Here, $\mu(g)=\mu(b)=0.5, u(b, T)=u(g, F)=-1, \lambda=1$.

Theorems & Definitions (11)

  • Remark 1
  • Definition 1: $\epsilon$-DP
  • Proposition 1: Responsible Developer's Strategy
  • Proposition 2
  • Remark 2
  • Proposition 3
  • Proposition 4
  • proof
  • Remark 3
  • Remark 4
  • ...and 1 more