Decoupled Conformal Optimisation: Efficient Prediction Sets via Independent Tuning and Calibration

Bayesian conformal optimisation methods often use the same held-out data both to search for efficient prediction sets and to certify coverage or risk. This coupling is natural for high-probability risk-control guarantees, but it is not necessary when the target is standard finite-sample marginal conformal coverage. We propose Decoupled Conformal Optimisation (DCO), a train-tune-calibrate design principle that uses an independent tuning split for efficiency-oriented structural selection and a fresh calibration split for the final conformal quantile. Conditional on the tuned structure, standard split-conformal exchangeability yields finite-sample marginal coverage for any candidate class, without a confidence parameter or multiple-testing correction. DCO therefore targets a different finite-sample guarantee from PAC-style methods: marginal conformal coverage rather than high-probability risk control. Under consistency assumptions on the coupled risk bound, the two approaches nevertheless converge to the same population threshold. Across classification and regression benchmarks, including ImageNet-A, CIFAR-100, Diabetes, California Housing, and Concrete, DCO tracks the nominal coverage level closely while often reducing average prediction-set size or interval width relative to PAC-style calibration. On ImageNet-A, for example, the average set size decreases from $26.52$ to $25.26$ and the 95th-percentile set size from $58.95$ to $53.73$; on Diabetes, the average interval width decreases from $2.098$ to $1.914$.

Bayesian Conformal Prediction as a Decision Risk Problem

Bayesian posterior predictive densities as non-conformity scores and Bayesian quadrature are used to estimate and minimise the expected prediction set size. Operating within a split conformal framework, BCP provides valid coverage guarantees and demonstrates reliable empirical coverage under model misspecification. Across regression and classification tasks, including distribution-shifted settings such as ImageNet-A, BCP yields prediction sets of comparable size to split conformal prediction, while exhibiting substantially lower run-to-run variability in set size. In sparse regression with nominal coverage of 80 percent, BCP achieves 81 percent empirical coverage under a misspecified prior, whereas Bayesian credible intervals under-cover at 49 percent.