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Concentrated Differential Privacy

Cynthia Dwork, Guy N. Rothblum

TL;DR

This work introduces Concentrated Differential Privacy (CDP), a relaxation of Differential Privacy that keeps the privacy loss distributed with a controllable mean μ and a subgaussian tail parameter τ, enabling tighter cumulative privacy guarantees under composition. CDP provides an advanced-composition–like guarantee: k CDP mechanisms compose to (Σμ_i, sqrt(Στ_i^2)), allowing much better accuracy for large numbers of analyses. It shows that Gaussian mechanisms achieve CDP with explicit parameters, and proves that any ε-DP mechanism is also CDP with improved mean loss and subgaussian concentration, while detailing tight group-privacy bounds. The paper also discusses tightness results via antipodal distributions, and notes subsequent work (e.g., Renyi-entropy based CDP) and the continued relevance of CDP for privacy-preserving data analysis with strong composition behavior.

Abstract

We introduce Concentrated Differential Privacy, a relaxation of Differential Privacy enjoying better accuracy than both pure differential privacy and its popular "(epsilon,delta)" relaxation without compromising on cumulative privacy loss over multiple computations.

Concentrated Differential Privacy

TL;DR

This work introduces Concentrated Differential Privacy (CDP), a relaxation of Differential Privacy that keeps the privacy loss distributed with a controllable mean μ and a subgaussian tail parameter τ, enabling tighter cumulative privacy guarantees under composition. CDP provides an advanced-composition–like guarantee: k CDP mechanisms compose to (Σμ_i, sqrt(Στ_i^2)), allowing much better accuracy for large numbers of analyses. It shows that Gaussian mechanisms achieve CDP with explicit parameters, and proves that any ε-DP mechanism is also CDP with improved mean loss and subgaussian concentration, while detailing tight group-privacy bounds. The paper also discusses tightness results via antipodal distributions, and notes subsequent work (e.g., Renyi-entropy based CDP) and the continued relevance of CDP for privacy-preserving data analysis with strong composition behavior.

Abstract

We introduce Concentrated Differential Privacy, a relaxation of Differential Privacy enjoying better accuracy than both pure differential privacy and its popular "(epsilon,delta)" relaxation without compromising on cumulative privacy loss over multiple computations.

Paper Structure

This paper contains 25 sections, 18 theorems, 93 equations.

Table of Contents

  1. Introduction
  2. A New Relaxation.
  3. Recent Developments
  4. Tightness.
  5. Subsequent Work.
  6. Preliminaries
  7. Divergence.
  8. Differential Privacy
  9. Privacy Loss as a Random Variable.
  10. Subgassian Random Variables
  11. Remarks.
  12. Concentrated Differential Privacy: Definition and Properties
  13. Guassian Mechanism Revisited.
  14. Composition
  15. Relationship to DP
  16. ...and 10 more sections

Key Result

Theorem 1.1

For all $\varepsilon, \delta, \delta' \ge 0$, the class of $(\varepsilon, \delta')$-differentially private mechanisms satisfies $( \sqrt{2k \ln (1/\delta)}\varepsilon + k\varepsilon(e^\varepsilon -1)/2, k\delta' + \delta)$-differential privacy under $k$-fold adaptive composition.

Theorems & Definitions (52)

  • Theorem 1.1
  • Remark 1.2
  • Remark 1.3
  • Definition 2.1: KL-Divergence
  • Definition 2.2: Max Divergence
  • Definition 2.3: $(\varepsilon,0)$-Differential Privacy ($(\varepsilon,0)$-DP) DworkMNS06
  • Definition 2.4: $(\varepsilon, \delta)$-Differential Privacy ($(\varepsilon,\delta)$-DP) DworkKMMN06
  • Definition 2.5: Subgaussian Random Variable Kahane60
  • Lemma 2.1: Subgaussian Concentration
  • proof
  • ...and 42 more