We design optimal privacy-enhancing and cost-efficient energy management strategies for consumers that are equipped with a rechargeable energy storage. The Kullback-Leibler divergence rate is used as privacy measure and the expected cost-saving rate is used as utility measure. The corresponding energy management strategy is designed by optimizing a weighted sum of both privacy and cost measures over a finite time horizon, which is achieved by formulating our problem into a belief-state Markov decision process problem. A computationally efficient approximated Q-learning method is proposed as a generalization to high-dimensional problems over an infinite time horizon. At last, we explicitly characterize a stationary policy that achieves the steady belief state over an infinite time horizon, which greatly simplifies the design of the privacy-preserving energy management strategy. The performance of the practical design approaches are finally illustrated in numerical experiments.

Motivated by recent works addressing adversarial attacks on deep reinforcement learning, a deception attack on linear quadratic Gaussian control is studied in this paper. In the considered attack model, the adversary can manipulate the observation of the agent subject to a mutual information constraint. The adversarial problem is formulated as a novel dynamic cheap talk game to capture the strategic interaction between the adversary and the agent, the asymmetry of information availability, and the system dynamics. Necessary and sufficient conditions are provided for subgame perfect equilibria to exist in pure strategies and in behavioral strategies; and characteristics of the equilibria and the resulting control rewards are given. The results show that pure strategy equilibria are informative, while only babbling equilibria exist in behavioral strategies. Numerical results are shown to illustrate the impact of strategic adversarial interaction.

Robust adversarial learning is considered in the context of closed-loop control with adversarial signaling in this paper. Due to the nature of incomplete information of the control agent about the environment, the belief-dependent signaling game formulation is introduced in the dynamic system and a dynamic cheap talk game is formulated with belief-dependent strategies for both players. We show that the dynamic cheap talk game can further be reformulated as a particular stochastic game, where the states are beliefs of the environment and the actions are the adversarial manipulation strategies and control strategies. Furthermore, the bisimulation metric is proposed and studied for the dynamic cheap talk game, which provides an upper bound on the difference between values of different initial beliefs in the zero-sum equilibrium.

Privacy against an adversary (AD) that tries to detect the underlying privacy-sensitive data distribution is studied. The original data sequence is assumed to come from one of the two known distributions, and the privacy leakage is measured by the probability of error of the binary hypothesis test carried out by the AD. A management unit (MU) is allowed to manipulate the original data sequence in an online fashion while satisfying an average distortion constraint. The goal of the MU is to maximize the minimal type II probability of error subject to a constraint on the type I probability of error assuming an adversarial Neyman-Pearson test, or to maximize the minimal error probability assuming an adversarial Bayesian test. The asymptotic exponents of the maximum minimal type II probability of error and the maximum minimal error probability are shown to be characterized by a Kullback-Leibler divergence rate and a Chernoff information rate, respectively. Privacy performances of particular management policies, the memoryless hypothesis-aware policy and the hypothesis-unaware policy with memory, are compared. The proposed formulation can also model adversarial example generation with minimal data manipulation to fool classifiers. At last, the results are applied to a smart meter privacy problem, where the user's energy consumption is manipulated by adaptively using a renewable energy source in order to hide user's activity from the energy provider.

Hypothesis testing is the fundamental theory behind decision-making and therefore plays a critical role in information systems. A prominent example is machine learning, which is currently developed and applied to a wide range of applications. However, besides the utilities, hypothesis testing can also be implemented for an illegitimate purpose to infer on people’s privacy. Thus, the development of hypothesis testing techniques further increases the privacy leakage risks. Accordingly, the research on privacy-by-design techniques that enhance the privacy against adversarial hypothesis testing receives more and more attention recently. In this chapter, the problem of privacy against adversarial hypothesis testing is formulated in the presence of a distortion source. Information-theoretic fundamental bounds on the optimal privacy performance and corresponding privacy-enhancing technologies are first discussed under the assumption of independent and identically distributed adversarial observations. The discussion is then extended to considering a privacy problem model with memory. In the end, applications of the theoretic results and privacy-enhancing technologies to the smart meter privacy problem are illustrated.

The design of optimal energy management strategies that trade-off consumers' privacy and expected energy cost by using an energy storage is studied. The Kullback-Leibler divergence rate is used to assess the privacy risk of the unauthorized testing on consumers' behavior. We further show how this design problem can be formulated as a belief state Markov decision process problem so that standard tools of the Markov decision process framework can be utilized, and the optimal solution can be obtained by using Bellman dynamic programming. Finally, we illustrate the privacy-enhancement and cost-saving by numerical examples. 

In this paper, the privacy leakage problem in an eavesdropped parallel distributed binary hypothesis test network is considered. A novel Neyman–Pearson test-operational privacy leakage measure is proposed and a privacy-constrained distributed Neyman–Pearson test problem is formulated. Such privacy-constrained distributed Neyman–Pearson test network is designed to optimize the Neyman–Pearson test performance and meanwhile to satisfy a desired suppression constraint on the privacy leakage. This study characterizes the privacy-constrained distributed Neyman–Pearson test network design and particularly identifies the sufficiency of deterministic likelihood-ratio test for optimality. These results help to simplify the optimal design problem of a privacy-constrained distributed Neyman–Pearson test network. Numerical results are presented to show the trade-off between the test performance and privacy leakage in privacy-constrained distributed Neyman–Pearson test networks.

Privacy-preserving energy management is studied in the presence of a renewable energy source. It is assumed that the energy demand/supply from the energy provider is tracked by a smart meter. The resulting privacy leakage is measured through the probabilities of error in a binary hypothesis test, which tries to detect the consumer behavior based on the meter readings. An optimal privacy-preserving energy management policy maximizes the minimal Type II probability of error subject to a constraint on the Type I probability of error. When the privacy-preserving energy management policy is based on all the available information of energy demands, energy supplies, and hypothesis, the asymptotic exponential decay rate of the maximum minimal Type II probability of error is characterized by a divergence rate expression. Two special privacy-preserving energy management policies, the memoryless hypothesis-aware policy and the hypothesis-unaware policy with memory, are then considered and their performances are compared. Further, it is shown that the energy supply alphabet can be constrained to the energy demand alphabet without loss of optimality for the evaluation of a single-letter-divergence privacy-preserving guarantee.

In this paper, an energy flow control strategy to reduce the smart meter privacy leakage is studied. The considered smart grid is equipped with an energy storage device. The privacy leakage is modeled as optimal Bayesian detections on the behaviors of the consumer made by an authorized adversary. To evaluate the privacy risk, a Bayesian detection-operational privacy leakage metric is proposed. The design of an optimal privacy-preserving energy control strategy can be formulated as a belief state MDP problem. Therefore, standard methods and algorithms can be utilized to obtain or to approximate the optimal control strategy. A simplified problem to design an instantaneous optimal privacy-preserving control strategy is also considered. It is shown that the problem of the instantaneous optimal control strategy design can be formulated as a set of linear programmings.

In this paper, we study the problem of privacy information leakage in a smart grid. The privacy risk is assumed to be caused by an unauthorized binary hypothesis testing of the consumer's behaviour based on the smart meter readings of energy supplies from the energy provider. Another energy supplies are produced by an alternative energy source. A controller equipped with an energy storage device manages the energy inflows to satisfy the energy demand of the consumer. We study the optimal energy control strategy which minimizes the asymptotic exponential decay rate of the minimum Type II error probability in the unauthorized hypothesis testing to suppress the privacy risk. Our study shows that the cardinality of the energy supplies from the energy provider for the optimal control strategy is no more than two. This result implies a simple objective of the optimal energy control strategy. When additional side information is available for the adversary, the optimal control strategy and privacy risk are compared with the case of leaking smart meter readings to the adversary only.