arXiv subjects

Shuo Han

Publications and source records attributed to Shuo Han.

96 records · Page 6Linked to original sources

arXiv2015

Optimality of the Laplace Mechanism in Differential Privacy

In the highly interconnected realm of Internet of Things, exchange of sensitive information raises severe privacy concerns. The Laplace mechanism -- adding Laplace-distributed artificial noise to sensitive data -- is one of the widely used methods of providing privacy guarantees within the framework of differential privacy. In this work, we present Lipschitz privacy, a slightly tighter version of differential privacy. We prove that the Laplace mechanism is optimal in the sense that it minimizes the mean-squared error for identity queries which provide privacy with respect to the $\ell_{1}$-norm. In addition to the $\ell_{1}$-norm which respects individuals' participation, we focus on the use of the $\ell_{2}$-norm which provides privacy of high-dimensional data. A variation of the Laplace mechanism is proven to have the optimal mean-squared error from the identity query. Finally, the optimal mechanism for the scenario in which individuals submit their high-dimensional sensitive data is derived.

cs.CR↗

arXiv2015

Gradual Release of Sensitive Data under Differential Privacy

We introduce the problem of releasing sensitive data under differential privacy when the privacy level is subject to change over time. Existing work assumes that privacy level is determined by the system designer as a fixed value before sensitive data is released. For certain applications, however, users may wish to relax the privacy level for subsequent releases of the same data after either a re-evaluation of the privacy concerns or the need for better accuracy. Specifically, given a database containing sensitive data, we assume that a response $y_1$ that preserves $ε_{1}$-differential privacy has already been published. Then, the privacy level is relaxed to $ε_2$, with $ε_2 > ε_1$, and we wish to publish a more accurate response $y_2$ while the joint response $(y_1, y_2)$ preserves $ε_2$-differential privacy. How much accuracy is lost in the scenario of gradually releasing two responses $y_1$ and $y_2$ compared to the scenario of releasing a single response that is $ε_{2}$-differentially private? Our results show that there exists a composite mechanism that achieves \textit{no loss} in accuracy. We consider the case in which the private data lies within $\mathbb{R}^{n}$ with an adjacency relation induced by the $\ell_{1}$-norm, and we focus on mechanisms that approximate identity queries. We show that the same accuracy can be achieved in the case of gradual release through a mechanism whose outputs can be described by a \textit{lazy Markov stochastic process}. This stochastic process has a closed form expression and can be efficiently sampled. Our results are applicable beyond identity queries. To this end, we demonstrate that our results can be applied in several cases, including Google's RAPPOR project, trading of sensitive data, and controlled transmission of private data in a social network.

cs.CR↗

arXiv2015

Optimal control in Markov decision processes via distributed optimization

Optimal control synthesis in stochastic systems with respect to quantitative temporal logic constraints can be formulated as linear programming problems. However, centralized synthesis algorithms do not scale to many practical systems. To tackle this issue, we propose a decomposition-based distributed synthesis algorithm. By decomposing a large-scale stochastic system modeled as a Markov decision process into a collection of interacting sub-systems, the original control problem is formulated as a linear programming problem with a sparse constraint matrix, which can be solved through distributed optimization methods. Additionally, we propose a decomposition algorithm which automatically exploits, if exists, the modular structure in a given large-scale system. We illustrate the proposed methods through robotic motion planning examples.

eess.SY↗

arXiv2014

Data-Driven Allocation of Vaccines for Controlling Epidemic Outbreaks

We propose a mathematical framework, based on conic geometric programming, to control a susceptible-infected-susceptible viral spreading process taking place in a directed contact network with unknown contact rates. We assume that we have access to time series data describing the evolution of the spreading process observed by a collection of sensor nodes over a finite time interval. We propose a data-driven robust convex optimization framework to find the optimal allocation of protection resources (e.g., vaccines and/or antidotes) to eradicate the viral spread at the fastest possible rate. In contrast to current network identification heuristics, in which a single network is identified to explain the observed data, we use available data to define an uncertainty set containing all networks that are coherent with empirical observations. Our characterization of this uncertainty set of networks is tractable in the context of conic geometric programming, recently proposed by Chandrasekaran and Shah, which allows us to efficiently find the optimal allocation of resources to control the worst-case spread that can take place in the uncertainty set of networks. We illustrate our approach in a transportation network from which we collect partial data about the dynamics of a hypothetical epidemic outbreak over a finite period of time.

math.OC↗

arXiv2014

Differentially Private Distributed Constrained Optimization

Many resource allocation problems can be formulated as an optimization problem whose constraints contain sensitive information about participating users. This paper concerns solving this kind of optimization problem in a distributed manner while protecting the privacy of user information. Without privacy considerations, existing distributed algorithms normally consist in a central entity computing and broadcasting certain public coordination signals to participating users. However, the coordination signals often depend on user information, so that an adversary who has access to the coordination signals can potentially decode information on individual users and put user privacy at risk. We present a distributed optimization algorithm that preserves differential privacy, which is a strong notion that guarantees user privacy regardless of any auxiliary information an adversary may have. The algorithm achieves privacy by perturbing the public signals with additive noise, whose magnitude is determined by the sensitivity of the projection operation onto user-specified constraints. By viewing the differentially private algorithm as an implementation of stochastic gradient descent, we are able to derive a bound for the suboptimality of the algorithm. We illustrate the implementation of our algorithm via a case study of electric vehicle charging. Specifically, we derive the sensitivity and present numerical simulations for the algorithm. Through numerical simulations, we are able to investigate various aspects of the algorithm when being used in practice, including the choice of step size, number of iterations, and the trade-off between privacy level and suboptimality.

math.OC↗

arXiv2014

Differentially Private Convex Optimization with Piecewise Affine Objectives

Differential privacy is a recently proposed notion of privacy that provides strong privacy guarantees without any assumptions on the adversary. The paper studies the problem of computing a differentially private solution to convex optimization problems whose objective function is piecewise affine. Such problem is motivated by applications in which the affine functions that define the objective function contain sensitive user information. We propose several privacy preserving mechanisms and provide analysis on the trade-offs between optimality and the level of privacy for these mechanisms. Numerical experiments are also presented to evaluate their performance in practice.

math.OC↗