  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.
