On Design of Optimal Smart Meter Privacy Control Strategy Against Adversarial Map Detection

We study the optimal control problem of the maximum a posteriori (MAP) state sequence detection of an adversary using smart meter data. The privacy leakage is measured using the Bayesian risk and the privacy-enhancing control is achieved in real-time using an energy storage system. The control strategy is designed to minimize the expected performance of a non-causal adversary at each time instant. With a discrete-state Markov model, we study two detection problems: when the adversary is unaware or aware of the control. We show that the adversary in the former case can be controlled optimally. In the latter case, where the optimal control problem is shown to be non-convex, we propose an adaptive-grid approximation algorithm to obtain a sub-optimal strategy with reduced complexity. Although this work focuses on privacy in smart meters, it can be generalized to other sensor networks.