Decision making under privacy restrictions

Cyber physical systems rely on the joint functioning of information and physical systems are vulnerable to information leakage through the observable outputs of the internal decision making mechanism. In particular, if an external observer has access to the outputs of the cyber system, then critical information can be inferred about the internal states of the physical system and consequently compromise user privacy. In this work, a mathematical framework based on a Markov Process model is proposed to study the process of decision making with requirements on privacy of internal states. Modelling state privacy using information theoretic equivocation, the problem is shown to reduce to a ρ-POMDP where the rewards exhibit non linear dependence on beliefs. Sub optimal strategies are investigated that are computationally tractable, and in special cases, analytically characterizable. Methods to compute upper bounds demonstrating the fundamental tradeoff between privacy and utility are also provided. A two state example is discussed to showcase the results.