Conditional Validity for Adaptive Modality Acquisition: When the Policy Chooses Its Own Calibration Group

Abstract

A multimodal system may begin inference while holding only some of its inputs and may acquire the rest at a cost. With adaptive acquisition, the policy determines which inputs are ultimately observed, so we state risk control conditional on that terminal input pattern. Conditional calibration typically assumes that the grouping map is fixed independently of the calibration sample, a condition that policy-induced grouping does not satisfy. We characterize when pattern-conditional risk control remains valid and give two finite-sample constructions: threshold-free routing with calibration applied at the terminal pattern, and simultaneous validation of complete policy-pattern pairs, which lets calibration data select the deployed policy. A counterexample shows that validity proved for a calibration-independent grouping map need not transfer once the policy makes the terminal group calibration-dependent. We call the resulting method RouteCert. On a clinical electrocardiogram task with a staged, cost-ordered lead protocol, the deployed policy answers 71.2% of held-out patients, with an observed 7.4% disagreement with the cardiologist's diagnosis at 48.8% of the prespecified ordinal cost of acquiring each stage, and all three acquisition stages are validated separately. On masked multimodal benchmarks, validating pointwise at each terminal pattern holds observed worst-pattern selective risk, measured against the full-information reference decision rather than the true label, at 0.034, where a pooled design reaches 0.145 against a 0.10 cap, at a comparable answered fraction (0.350 vs 0.342); under the budget-matched simultaneous comparison, the answered fraction falls to 0.305.

23 pages, 4 figures, 14 tables. Includes appendix with full proofs