Geometry of Sensitivity: Twice Sampling and Hybrid Clipping in Differential Privacy with Optimal Gaussian Noise and Application to Deep Learning

• URL: http://arxiv.org/abs/2309.02672v2
• Date: Thu, 28 Sep 2023 12:49:24 GMT
• Title: Geometry of Sensitivity: Twice Sampling and Hybrid Clipping in Differential Privacy with Optimal Gaussian Noise and Application to Deep Learning
• Authors: Hanshen Xiao, Jun Wan, Srinivas Devadas,
• Abstract summary: We study the problem of the construction of optimal randomization in Differential Privacy. Finding the minimal perturbation for properly-selected sensitivity sets is a central problem in DP research.
• Score: 18.92302645198466
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the fundamental problem of the construction of optimal randomization in Differential Privacy. Depending on the clipping strategy or additional properties of the processing function, the corresponding sensitivity set theoretically determines the necessary randomization to produce the required security parameters. Towards the optimal utility-privacy tradeoff, finding the minimal perturbation for properly-selected sensitivity sets stands as a central problem in DP research. In practice, l_2/l_1-norm clippings with Gaussian/Laplace noise mechanisms are among the most common setups. However, they also suffer from the curse of dimensionality. For more generic clipping strategies, the understanding of the optimal noise for a high-dimensional sensitivity set remains limited. In this paper, we revisit the geometry of high-dimensional sensitivity sets and present a series of results to characterize the non-asymptotically optimal Gaussian noise for R\'enyi DP (RDP). Our results are both negative and positive: on one hand, we show the curse of dimensionality is tight for a broad class of sensitivity sets satisfying certain symmetry properties; but if, fortunately, the representation of the sensitivity set is asymmetric on some group of orthogonal bases, we show the optimal noise bounds need not be explicitly dependent on either dimension or rank. We also revisit sampling in the high-dimensional scenario, which is the key for both privacy amplification and computation efficiency in large-scale data processing. We propose a novel method, termed twice sampling, which implements both sample-wise and coordinate-wise sampling, to enable Gaussian noises to fit the sensitivity geometry more closely. With closed-form RDP analysis, we prove twice sampling produces asymptotic improvement of the privacy amplification given an additional infinity-norm restriction, especially for small sampling rate.

Related papers

• Accelerated zero-order SGD under high-order smoothness and overparameterized regime [79.85163929026146]
  We present a novel gradient-free algorithm to solve convex optimization problems. Such problems are encountered in medicine, physics, and machine learning. We provide convergence guarantees for the proposed algorithm under both types of noise.
  arXiv  Detail & Related papers  (2024-11-21T10:26:17Z)
• Some Constructions of Private, Efficient, and Optimal $K$-Norm and Elliptic Gaussian Noise [54.34628844260993]
  Differentially private computation often begins with a bound on some $d$-dimensional statistic's sensitivity. For pure differential privacy, the $K$-norm mechanism can improve on this approach using a norm tailored to the statistic's sensitivity space. This paper solves both problems for the simple statistics of sum, count, and vote.
  arXiv  Detail & Related papers  (2023-09-27T17:09:36Z)
• One-Dimensional Deep Image Prior for Curve Fitting of S-Parameters from Electromagnetic Solvers [57.441926088870325]
  Deep Image Prior (DIP) is a technique that optimized the weights of a randomly-d convolutional neural network to fit a signal from noisy or under-determined measurements. Relative to publicly available implementations of Vector Fitting (VF), our method shows superior performance on nearly all test examples.
  arXiv  Detail & Related papers  (2023-06-06T20:28:37Z)
• Practical Differentially Private Hyperparameter Tuning with Subsampling [8.022555128083026]
  We propose a new class of differentially private (DP) machine learning (ML) algorithms, where the number of random search samples is randomized itself. We focus on lowering both the DP bounds and the computational cost of these methods by using only a random subset of the sensitive data. We provide a R'enyi differential privacy analysis for the proposed method and experimentally show that it consistently leads to better privacy-utility trade-off.
  arXiv  Detail & Related papers  (2023-01-27T21:01:58Z)
• Normalized/Clipped SGD with Perturbation for Differentially Private Non-Convex Optimization [94.06564567766475]
  DP-SGD and DP-NSGD mitigate the risk of large models memorizing sensitive training data. We show that these two algorithms achieve similar best accuracy while DP-NSGD is comparatively easier to tune than DP-SGD.
  arXiv  Detail & Related papers  (2022-06-27T03:45:02Z)
• High-Dimensional Simulation Optimization via Brownian Fields and Sparse Grids [14.15772050249329]
  High-dimensional simulation optimization is notoriously challenging. We propose a new sampling algorithm that converges to a global optimal solution. We show that the proposed algorithm dramatically outperforms typical alternatives in practice.
  arXiv  Detail & Related papers  (2021-07-19T03:03:27Z)
• High Probability Complexity Bounds for Non-Smooth Stochastic Optimization with Heavy-Tailed Noise [51.31435087414348]
  It is essential to theoretically guarantee that algorithms provide small objective residual with high probability. Existing methods for non-smooth convex optimization have complexity bounds with dependence on confidence level. We propose novel stepsize rules for two methods with gradient clipping.
  arXiv  Detail & Related papers  (2021-06-10T17:54:21Z)
• Adaptive and Oblivious Randomized Subspace Methods for High-Dimensional Optimization: Sharp Analysis and Lower Bounds [37.03247707259297]
  A suitable adaptive subspace can be generated by sampling a correlated random matrix whose second order statistics mirror the input data. We show that the relative error of the randomized approximations can be tightly characterized in terms of the spectrum of the data matrix. Experimental results show that the proposed approach enables significant speed ups in a wide variety of machine learning and optimization problems.
  arXiv  Detail & Related papers  (2020-12-13T13:02:31Z)
• Sparse Representations of Positive Functions via First and Second-Order Pseudo-Mirror Descent [15.340540198612823]
  We consider expected risk problems when the range of the estimator is required to be nonnegative. We develop first and second-order variants of approximation mirror descent employing emphpseudo-gradients. Experiments demonstrate favorable performance on ingeneous Process intensity estimation in practice.
  arXiv  Detail & Related papers  (2020-11-13T21:54:28Z)
• Effective Dimension Adaptive Sketching Methods for Faster Regularized Least-Squares Optimization [56.05635751529922]
  We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching. We consider two of the most popular random embeddings, namely, Gaussian embeddings and the Subsampled Randomized Hadamard Transform (SRHT)
  arXiv  Detail & Related papers  (2020-06-10T15:00:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.