  Representation learning is increasingly employed to generate representations
that are predictive across multiple downstream tasks. The development of
representation learning algorithms that provide strong fairness guarantees is
thus important because it can prevent unfairness towards disadvantaged groups
for all downstream prediction tasks. To prevent unfairness towards
disadvantaged groups in all downstream tasks, it is crucial to provide
representation learning algorithms that provide fairness guarantees. In this
paper, we formally define the problem of learning representations that are fair
with high confidence. We then introduce the Fair Representation learning with
high-confidence Guarantees (FRG) framework, which provides high-confidence
guarantees for limiting unfairness across all downstream models and tasks, with
user-defined upper bounds. After proving that FRG ensures fairness for all
downstream models and tasks with high probability, we present empirical
evaluations that demonstrate FRG's effectiveness at upper bounding unfairness
for multiple downstream models and tasks.
