  As predictive models are increasingly being employed to make consequential
decisions, there is a growing emphasis on developing techniques that can
provide algorithmic recourse to affected individuals. While such recourses can
be immensely beneficial to affected individuals, potential adversaries could
also exploit these recourses to compromise privacy. In this work, we make the
first attempt at investigating if and how an adversary can leverage recourses
to infer private information about the underlying model's training data. To
this end, we propose a series of novel membership inference attacks which
leverage algorithmic recourse. More specifically, we extend the prior
literature on membership inference attacks to the recourse setting by
leveraging the distances between data instances and their corresponding
counterfactuals output by state-of-the-art recourse methods. Extensive
experimentation with real world and synthetic datasets demonstrates significant
privacy leakage through recourses. Our work establishes unintended privacy
leakage as an important risk in the widespread adoption of recourse methods.
