Khái niệm cốt lõi
The author establishes the "privacy amplification by iteration" phenomenon in f-DP, enabling convergent privacy analysis for noisy optimization algorithms. The approach involves constructing shifted interpolated processes to achieve tighter privacy bounds.
Tóm tắt
The content discusses the improvement of privacy analysis for differentially private machine learning algorithms. It introduces the concept of shifted interpolation in f-DP to quantify privacy leakage more accurately and efficiently. The paper presents theoretical methodologies and numerical examples to demonstrate the effectiveness of the proposed approach.
Noisy gradient descent is a common algorithm for private optimization, but quantifying its differential privacy remains a challenge. The paper introduces shifted interpolation processes to enhance privacy analysis, particularly in strongly convex optimization settings. By establishing convergent f-DP bounds, the study provides insights into improving privacy guarantees for various optimization scenarios.
The research extends to different batch types and optimization settings, showcasing versatile applications of the proposed methodology. Through detailed theoretical explanations and practical examples, it highlights the significance of accurate privacy quantification in machine learning algorithms.
Key metrics or figures:
Noisy gradient descent is µ-GDP where µ = L / (nσ√t) (Theorem 4.1)
NoisyGD is µ-GDP where µ = 1 / σ * sqrt(3LDηn + L^2 / n^2) * DnηL (Theorem 4.3)
NoisyCGD is µ-GDP where µ = L / bσ * sqrt((1 + c^2l^-2)/(1 - c^2)(1 - cl)^2(1 - cl(E-1))/(1 + cl(E-1))) (Theorem 4.5)
Thống kê
No key metrics or figures provided in the analyzed content.
Trích dẫn
"Noisy gradient descent and its variants are predominant algorithms for differentially private machine learning."
"The paper improves over previous analyses by establishing 'privacy amplification by iteration' phenomenon."