Minimizing Information Leakage of Abrupt Changes in Stochastic Systems

This work investigates the problem of analyzing privacy of abrupt changes for general Markov processes. These processes may be affected by changes, or exogenous signals, that need to remain private. Privacy refers to the disclosure of information of these changes through observations of the underlying Markov chain. In contrast to previous work on privacy, we study the problem for an online sequence of data. We use theoretical tools from optimal detection theory to motivate a definition of online privacy based on the average amount of information per observation of the stochastic system in consideration. Two cases are considered: the full-information case, where the eavesdropper measures all but the signals that indicate a change, and the limited-information case, where the eavesdropper only measures the state of the Markov process. For both cases, we provide ways to derive privacy upper-bounds and compute policies that attain a higher privacy level. It turns out that the problem of computing privacy-aware policies is concave, and we conclude with some examples and numerical simulations for both cases.