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Register a new userLocal Differential Privacy Is Equivalent to Contraction of $E_gamma$-Divergence
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Added by
Shahab Asoodeh
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We investigate the local differential privacy (LDP) guarantees of a randomized privacy mechanism via its contraction properties. We first show that LDP constraints can be equivalently cast in terms of the contraction coefficient of the $E_gamma$-divergence. We then use this equivalent formula to express LDP guarantees of privacy mechanisms in terms of contraction coefficients of arbitrary $f$-divergences. When combined with standard estimation-theoretic tools (such as Le Cams and Fanos converse methods), this result allows us to study the trade-off between privacy and utility in several testing and minimax and Bayesian estimation problems.
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Contextual bandit algorithms are useful in personalized online decision-making. However, many applications such as personalized medicine and online advertising require the utilization of individual-specific information for effective learning, while users data should remain private from the server due to privacy concerns. This motivates the introduction of local differential privacy (LDP), a stringent notion in privacy, to contextual bandits. In this paper, we design LDP algorithms for stochastic generalized linear bandits to achieve the same regret bound as in non-privacy settings. Our main idea is to develop a stochastic gradient-based estimator and update mechanism to ensure LDP. We then exploit the flexibility of stochastic gradient descent (SGD), whose theoretical guarantee for bandit problems is rarely explored, in dealing with generalized linear bandits. We also develop an estimator and update mechanism based on Ordinary Least Square (OLS) for linear bandits. Finally, we conduct experiments with both simulation and real-world datasets to demonstrate the consistently superb performance of our algorithms under LDP constraints with reasonably small parameters $(varepsilon, delta)$ to ensure strong privacy protection.
This paper considers derivation of $f$-divergence inequalities via the approach of functional domination. Bounds on an $f$-divergence based on one or several other $f$-divergences are introduced, dealing with pairs of probability measures defined on arbitrary alphabets. In addition, a variety of bounds are shown to hold under boundedness assumptions on the relative information. The journal paper, which includes more approaches for the derivation of f-divergence inequalities and proofs, is available on the arXiv at https://arxiv.org/abs/1508.00335, and it has been published in the IEEE Trans. on Information Theory, vol. 62, no. 11, pp. 5973-6006, November 2016.
We consider the binary classification problem in a setup that preserves the privacy of the original sample. We provide a privacy mechanism that is locally differentially private and then construct a classifier based on the private sample that is universally consistent in Euclidean spaces. Under stronger assumptions, we establish the minimax rates of convergence of the excess risk and see that they are slower than in the case when the original sample is available.
Differential privacy has become a widely accepted notion of privacy, leading to the introduction and deployment of numerous privatization mechanisms. However, ensuring the privacy guarantee is an error-prone process, both in designing mechanisms and in implementing those mechanisms. Both types of errors will be greatly reduced, if we have a data-driven approach to verify privacy guarantees, from a black-box access to a mechanism. We pose it as a property estimation problem, and study the fundamental trade-offs involved in the accuracy in estimated privacy guarantees and the number of samples required. We introduce a novel estimator that uses polynomial approximation of a carefully chosen degree to optimally trade-off bias and variance. With $n$ samples, we show that this estimator achieves performance of a straightforward plug-in estimator with $n ln n$ samples, a phenomenon referred to as effective sample size amplification. The minimax optimality of the proposed estimator is proved by comparing it to a matching fundamental lower bound.
In this paper, we study the problem of publishing a stream of real-valued data satisfying differential privacy (DP). One major challenge is that the maximal possible value can be quite large; thus it is necessary to estimate a threshold so that numbers above it are truncated to reduce the amount of noise that is required to all the data. The estimation must be done based on the data in a private fashion. We develop such a method that uses the Exponential Mechanism with a quality function that approximates well the utility goal while maintaining a low sensitivity. Given the threshold, we then propose a novel online hierarchical method and several post-processing techniques. Building on these ideas, we formalize the steps into a framework for private publishing of stream data. Our framework consists of three components: a threshold optimizer that privately estimates the threshold, a perturber that adds calibrated noises to the stream, and a smoother that improves the result using post-processing. Within our framework, we design an algorithm satisfying the more stringent setting of DP called local DP (LDP). To our knowledge, this is the first LDP algorithm for publishing streaming data. Using four real-world datasets, we demonstrate that our mechanism outperforms the state-of-the-art by a factor of 6-10 orders of magnitude in terms of utility (measured by the mean squared error of answering a random range query).
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