  As the use of machine learning models in real world high-stakes decision
settings continues to grow, it is highly important that we are able to audit
and control for any potential fairness violations these models may exhibit
towards certain groups. To do so, one naturally requires access to sensitive
attributes, such as demographics, gender, or other potentially sensitive
features that determine group membership. Unfortunately, in many settings, this
information is often unavailable. In this work we study the well known
\emph{equalized odds} (EOD) definition of fairness. In a setting without
sensitive attributes, we first provide tight and computable upper bounds for
the EOD violation of a predictor. These bounds precisely reflect the worst
possible EOD violation. Second, we demonstrate how one can provably control the
worst-case EOD by a new post-processing correction method. Our results
characterize when directly controlling for EOD with respect to the predicted
sensitive attributes is -- and when is not -- optimal when it comes to
controlling worst-case EOD. Our results hold under assumptions that are milder
than previous works, and we illustrate these results with experiments on
synthetic and real datasets.
