  This paper introduces a boosted conformal procedure designed to tailor
conformalized prediction intervals toward specific desired properties, such as
enhanced conditional coverage or reduced interval length. We employ machine
learning techniques, notably gradient boosting, to systematically improve upon
a predefined conformity score function. This process is guided by carefully
constructed loss functions that measure the deviation of prediction intervals
from the targeted properties. The procedure operates post-training, relying
solely on model predictions and without modifying the trained model (e.g., the
deep network). Systematic experiments demonstrate that starting from
conventional conformal methods, our boosted procedure achieves substantial
improvements in reducing interval length and decreasing deviation from target
conditional coverage.
