  Conventional frequentist learning is known to yield poorly calibrated models
that fail to reliably quantify the uncertainty of their decisions. Bayesian
learning can improve calibration, but formal guarantees apply only under
restrictive assumptions about correct model specification. Conformal prediction
(CP) offers a general framework for the design of set predictors with
calibration guarantees that hold regardless of the underlying data generation
mechanism. However, when training data are limited, CP tends to produce large,
and hence uninformative, predicted sets. This paper introduces a novel
meta-learning solution that aims at reducing the set prediction size. Unlike
prior work, the proposed meta-learning scheme, referred to as meta-XB, (i)
builds on cross-validation-based CP, rather than the less efficient
validation-based CP; and (ii) preserves formal per-task calibration guarantees,
rather than less stringent task-marginal guarantees. Finally, meta-XB is
extended to adaptive non-conformal scores, which are shown empirically to
further enhance marginal per-input calibration.
