As machine learning is widely deployed, it is increasingly important to ensure that predictors will perform well not only on average (across the entire population), but also on specific socially salient subgroups. In this talk, I will present Outcome Indistinguishability (OI), a new learning paradigm that draws on the concept of computational indistinguishability. I will demonstrate that OI can be used to obtain guarantees that go beyond standard loss minimization, such as simultaneous loss minimization across subgroups.