  We consider the problem of distribution-free conformal prediction and the
criterion of group conditional validity. This criterion is motivated by many
practical scenarios including hidden stratification and group fairness.
Existing methods achieve such guarantees under either restrictive grouping
structure or distributional assumptions, or they are overly-conservative under
heteroskedastic noise. We propose a simple reduction to the problem of
achieving validity guarantees for individual populations by leveraging
algorithms for a problem called multi-group learning. This allows us to port
theoretical guarantees from multi-group learning to obtain obtain sample
complexity guarantees for conformal prediction. We also provide a new algorithm
for multi-group learning for groups with hierarchical structure. Using this
algorithm in our reduction leads to improved sample complexity guarantees with
a simpler predictor structure.
