Privacy Games: Optimal User-Centric Data Obfuscation

In this paper, we design user-centric obfuscation mechanisms that impose the minimum utility loss for guaranteeing user's privacy. We optimize utility subject to a joint guarantee of differential privacy (indistinguishability) and distortion privacy (inference error). This double shield of protection limits the information leakage through obfuscation mechanism as well as the posterior inference. We show that the privacy achieved through joint differential-distortion mechanisms against optimal attacks is as large as the maximum privacy that can be achieved by either of these mechanisms separately. Their utility cost is also not larger than what either of the differential or distortion mechanisms imposes. We model the optimization problem as a leader-follower game between the designer of obfuscation mechanism and the potential adversary, and design adaptive mechanisms that anticipate and protect against optimal inference algorithms. Thus, the obfuscation mechanism is optimal against any inference algorithm.