Decision-Focused Calibration with Adaptive Conformal Predictive Distributions

Decision-focused learning can improve downstream decisions, but a predictive distribution trained for a particular task may misrepresent the outcomes it is meant to predict. Conversely, a distribution trained solely for predictive accuracy may miss features that matter most to the decision. We study how to adapt predictive distributions to decisions subject to a conformal calibration constraint. Our key observation is that a nonconformity score separates the remaining modeling problem into two parts: how probability varies across score levels with the context, and which outcomes occur within each level. We propose AdaCF, an adaptive conformal flow that learns both parts, optionally incorporates a downstream decision loss, and uses a rank-based correction to ensure finite-sample marginal validity under exchangeability. We decompose predictive error into the errors of the two learned components and bound regret for bounded decision losses in terms of that error. On synthetic problems and electricity price data, AdaCF improves predictive fidelity and decision quality over standard conformal flows while preserving validity.