Data-driven systems are gathering increasing amounts of data from users, and sensitive user data requires privacy protections. In some cases, the data gathered is non-numerical or symbolic, and conventional approaches to privacy, e.g., adding noise, do not apply, though such systems still require privacy protections. Accordingly, we present a novel differential privacy framework for protecting trajectories generated by symbolic systems. These trajectories can be represented as words or strings over a finite alphabet. We develop new differential privacy mechanisms that approximate a sensitive word using a random word that is likely to be near it. An offline mechanism is implemented efficiently using a Modified Hamming Distance Automaton to generate whole privatized output words over a finite time horizon. Then, an online mechanism is implemented by taking in a sensitive symbol and generating a randomized output symbol at each timestep. This work is extended to Markov chains to generate differentially private state sequences that a given Markov chain could have produced. Statistical accuracy bounds are developed to quantify the accuracy of these mechanisms, and numerical results validate the accuracy of these techniques for strings of English words.
In this paper, we develop a privacy implementation for symbolic control systems. Such systems generate sequences of non-numerical data, and these sequences can be represented by words or strings over a finite alphabet. This work uses the framework of differential privacy, which is a statistical notion of privacy that makes it unlikely that privatized data will reveal anything meaningful about underlying sensitive data. To bring differential privacy to symbolic control systems, we develop an exponential mechanism that approximates a sensitive word using a randomly chosen word that is likely to …
In decision-making problems, the actions of an agent may reveal sensitive information that drives its decisions. For instance, a corporation's investment decisions may reveal its sensitive knowledge about market dynamics. To prevent this type of information leakage, we introduce a policy synthesis algorithm that protects the privacy of the transition probabilities in a Markov decision process. We use differential privacy as the mathematical definition of privacy. The algorithm first perturbs the transition probabilities using a mechanism that provides differential privacy. Then, based on the p…
In the literature of data privacy, differential privacy is the most popular model. An algorithm is differentially private if its outputs with and without any individual's data are indistinguishable. In this paper, we focus on data generated from a Markov chain and argue that Bayesian differential privacy (BDP) offers more meaningful guarantees in this context. Our main theoretical contribution is providing a mechanism for achieving BDP when data is drawn from a binary Markov chain. We improve on the state-of-the-art BDP mechanism and show that our mechanism provides the optimal noise-privacy t…
Pufferfish is a Bayesian privacy framework for designing and analyzing privacy mechanisms. It refines differential privacy, the current gold standard in data privacy, by allowing explicit prior knowledge in privacy analysis. Through these privacy frameworks, a number of privacy mechanisms have been developed in literature. In practice, privacy mechanisms often need be modified or adjusted to specific applications. Their privacy risks have to be re-evaluated for different circumstances. Moreover, computing devices only approximate continuous noises through floating-point computation, which is d…
Publishing trajectory data (individual's movement information) is very useful, but it also raises privacy concerns. To handle the privacy concern, in this paper, we apply differential privacy, the standard technique for data privacy, together with Markov chain model, to generate synthetic trajectories. We notice that existing studies all use Markov chain model and thus propose a framework to analyze the usage of the Markov chain model in this problem. Based on the analysis, we come up with an effective algorithm PrivTrace that uses the first-order and second-order Markov model adaptively. We e…
Implementations of the exponential mechanism in differential privacy often require sampling from intractable distributions. When approximate procedures like Markov chain Monte Carlo (MCMC) are used, the end result incurs costs to both privacy and accuracy. Existing work has examined these effects asymptotically, but implementable finite sample results are needed in practice so that users can specify privacy budgets in advance and implement samplers with exact privacy guarantees. In this paper, we use tools from ergodic theory and perfect simulation to design exact finite runtime sampling algor…
Cornell University（康奈尔大学）；University of Waterloo（滑铁卢大学）；Microsoft Research Redmond（微软雷德蒙德研究院）；University of Minnesota（明尼苏达大学）
We consider the problem of learning Markov Random Fields (including the prototypical example, the Ising model) under the constraint of differential privacy. Our learning goals include both structure learning, where we try to estimate the underlying graph structure of the model, as well as the harder goal of parameter learning, in which we additionally estimate the parameter on each edge. We provide algorithms and lower bounds for both problems under a variety of privacy constraints -- namely pure, concentrated, and approximate differential privacy. While non-privately, both learning goals enjo…
University of Halmstad（哈尔姆斯塔德大学）；Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所 HIIT）；University of Helsinki（赫尔辛基大学）；Aalto University（阿尔托大学）
Recent developments in differentially private (DP) machine learning and DP Bayesian learning have enabled learning under strong privacy guarantees for the training data subjects. In this paper, we further extend the applicability of DP Bayesian learning by presenting the first general DP Markov chain Monte Carlo (MCMC) algorithm whose privacy-guarantees are not subject to unrealistic assumptions on Markov chain convergence and that is applicable to posterior inference in arbitrary models. Our algorithm is based on a decomposition of the Barker acceptance test that allows evaluating the Rényi D…
Indian Institute of Science（印度科学理工学院）；Wayne State University（韦恩州立大学）
We study regret minimization in finite horizon tabular Markov decision processes (MDPs) under the constraints of differential privacy (DP). This is motivated by the widespread applications of reinforcement learning (RL) in real-world sequential decision making problems, where protecting users' sensitive and private information is becoming paramount. We consider two variants of DP -- joint DP (JDP), where a centralized agent is responsible for protecting users' sensitive data and local DP (LDP), where information needs to be protected directly on the user side. We first propose two general fram…
Tsinghua University（清华大学）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Reinforcement learning (RL) algorithms can be used to provide personalized services, which rely on users' private and sensitive data. To protect the users' privacy, privacy-preserving RL algorithms are in demand. In this paper, we study RL with linear function approximation and local differential privacy (LDP) guarantees. We propose a novel $(\varepsilon, δ)$-LDP algorithm for learning a class of Markov decision processes (MDPs) dubbed linear mixture MDPs, and obtains an $\tilde{\mathcal{O}}( d^{5/4}H^{7/4}T^{3/4}\left(\log(1/δ)\right)^{1/4}\sqrt{1/\varepsilon})$ regret, where $d$ is the dimen…
UC Santa Barbara（加州大学圣巴巴拉分校）；Northwestern University（西北大学）
Characterizing the privacy degradation over compositions, i.e., privacy accounting, is a fundamental topic in differential privacy (DP) with many applications to differentially private machine learning and federated learning. We propose a unification of recent advances (Renyi DP, privacy profiles, $f$-DP and the PLD formalism) via the \emph{characteristic function} ($ϕ$-function) of a certain \emph{dominating} privacy loss random variable. We show that our approach allows \emph{natural} adaptive composition like Renyi DP, provides \emph{exactly tight} privacy accounting like PLD, and can be (o…
Technical University of Munich（慕尼黑工业大学）；Imperial College London（帝国理工学院）
Differential privacy (DP) allows the quantification of privacy loss when the data of individuals is subjected to algorithmic processing such as machine learning, as well as the provision of objective privacy guarantees. However, while techniques such as individual Rényi DP (RDP) allow for granular, per-person privacy accounting, few works have investigated the impact of each input feature on the individual's privacy loss. Here we extend the view of individual RDP by introducing a new concept we call partial sensitivity, which leverages symbolic automatic differentiation to determine the influe…
MPI-SP（马克斯·普朗克安全与隐私研究所）；IMDEA Software Institute（IMDEA软件研究所）；University at Buffalo, SUNY（纽约州立大学布法罗分校）；U.C. San Diego（加州大学圣迭戈分校）
A fundamental result in differential privacy states that the privacy guarantees of a mechanism are preserved by any post-processing of its output. In this paper we investigate under what conditions stochastic post-processing can amplify the privacy of a mechanism. By interpreting post-processing as the application of a Markov operator, we first give a series of amplification results in terms of uniform mixing properties of the Markov process defined by said operator. Next we provide amplification bounds in terms of coupling arguments which can be applied in cases where uniform mixing is not av…
The University of Florida（佛罗里达大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
Privacy-aware multiagent systems must protect agents' sensitive data while simultaneously ensuring that agents accomplish their shared objectives. Towards this goal, we propose a framework to privatize inter-agent communications in cooperative multiagent decision-making problems. We study sequential decision-making problems formulated as cooperative Markov games with reach-avoid objectives. We apply a differential privacy mechanism to privatize agents' communicated symbolic state trajectories, and then we analyze tradeoffs between the strength of privacy and the team's performance. For a given…
Objective: Implement and assess personal health identifying information (PHI) substitution strategies and quantify their privacy preserving benefits. Materials and Methods: We implement and assess 3 different `Hiding in Plain Sight` (HIPS) strategies for PHI replacement including a standard Consistent replacement strategy, a Random replacement strategy and a novel Markov model-based strategy. We evaluate the privacy preserving benefits of these strategies on a synthetic PHI distribution and real clinical corpora from 2 different institutions using a range of false negative error rates (FNER). …
The offline reinforcement learning (RL) problem is often motivated by the need to learn data-driven decision policies in financial, legal and healthcare applications. However, the learned policy could retain sensitive information of individuals in the training data (e.g., treatment and outcome of patients), thus susceptible to various privacy risks. We design offline RL algorithms with differential privacy guarantees which provably prevent such risks. These algorithms also enjoy strong instance-dependent learning bounds under both tabular and linear Markov decision process (MDP) settings. Our …
Indian Institute of Technology Kanpur（印度理工学院坎普尔分校）；University of Wisconsin–Madison（威斯康星大学麦迪逊分校）
Differential privacy is a formal, mathematical definition of data privacy that has gained traction in academia, industry, and government. The task of correctly constructing differentially private algorithms is non-trivial, and mistakes have been made in foundational algorithms. Currently, there is no automated support for converting an existing, non-private program into a differentially private version. In this paper, we propose a technique for automatically learning an accurate and differentially private version of a given non-private program. We show how to solve this difficult program synth…
With the proliferation of mobile devices and the internet of things, developing principled solutions for privacy in time series applications has become increasingly important. While differential privacy is the gold standard for database privacy, many time series applications require a different kind of guarantee, and a number of recent works have used some form of inferential privacy to address these situations. However, a major barrier to using inferential privacy in practice is its lack of graceful composition -- even if the same or related sensitive data is used in multiple releases that ar…
