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Striking a Balance: An Optimal Mechanism Design for Heterogenous Differentially Private Data Acquisition for Logistic Regression

Ameya Anjarlekar, Rasoul Etesami, R. Srikant

TL;DR

The objective is to design a mechanism that optimizes a weighted combination of test loss, seller privacy, and payment, striking a balance between building a good privacy-preserving ML model and minimizing payments to the sellers.

Abstract

We address the challenge of solving machine learning tasks using data from privacy-sensitive sellers. Since the data is private, we design a data market that incentivizes sellers to provide their data in exchange for payments. Therefore our objective is to design a mechanism that optimizes a weighted combination of test loss, seller privacy, and payment, striking a balance between building a good privacy-preserving ML model and minimizing payments to the sellers. To achieve this, we first propose an approach to solve logistic regression with known heterogeneous differential privacy guarantees. Building on these results and leveraging standard mechanism design theory, we develop a two-step optimization framework. We further extend this approach to an online algorithm that handles the sequential arrival of sellers.

Striking a Balance: An Optimal Mechanism Design for Heterogenous Differentially Private Data Acquisition for Logistic Regression

TL;DR

The objective is to design a mechanism that optimizes a weighted combination of test loss, seller privacy, and payment, striking a balance between building a good privacy-preserving ML model and minimizing payments to the sellers.

Abstract

We address the challenge of solving machine learning tasks using data from privacy-sensitive sellers. Since the data is private, we design a data market that incentivizes sellers to provide their data in exchange for payments. Therefore our objective is to design a mechanism that optimizes a weighted combination of test loss, seller privacy, and payment, striking a balance between building a good privacy-preserving ML model and minimizing payments to the sellers. To achieve this, we first propose an approach to solve logistic regression with known heterogeneous differential privacy guarantees. Building on these results and leveraging standard mechanism design theory, we develop a two-step optimization framework. We further extend this approach to an online algorithm that handles the sequential arrival of sellers.
Paper Structure (27 sections, 9 theorems, 85 equations, 4 figures, 4 algorithms)

This paper contains 27 sections, 9 theorems, 85 equations, 4 figures, 4 algorithms.

Table of Contents

  1. Introduction
  2. Contributions and Organization
  3. Related Work
  4. Logistic Regression while Ensuring Heterogeneous Differential Privacy
  5. Differential Privacy
  6. Representing the Misclassification Error
  7. Mechanism Design Problem
  8. Buyer's Objective
  9. Solving the Mechanism Design Problem
  10. Discussion
  11. Performance Analysis
  12. Extension to Online Setting
  13. Numerical Results
  14. Offline Algorithm
  15. Online Algorithm
  16. ...and 12 more sections

Key Result

Proposition 2.2

For any $(\boldsymbol{a},\eta) \in \mathbb{F}$, the output of Algorithm alg:basic, denoted by $\hat{w}$, preserves $\boldsymbol{\epsilon} + \Delta$ differential privacy, where $\Delta = 2 \log(1 + \frac{k}{m \Lambda}).$

Figures (4)

  • Figure 1: Interaction between sellers and the platform
  • Figure 2: Mechanism Design Experiments
  • Figure 3: Online Algorithm Experiments
  • Figure 4: Hyperparameter Analysis

Theorems & Definitions (21)

  • Definition 2.1
  • Proposition 2.2
  • Remark 2.3
  • Theorem 2.4
  • Lemma 3.2
  • Theorem 3.3
  • Remark 4.1
  • Remark 4.2
  • Theorem 4.5
  • Theorem 5.1
  • ...and 11 more