Modern conformal forecasting systems often maintain several adaptive pipelines that differ in base forecasters, conformity scores, calibration windows, and update rules.
Comparing them is difficult because coverage is a hard constraint, whereas efficiency should be optimized only among feasible pipelines.
We formulate this problem as sequential inference for a stochastic constrained argmin.
At each time, the target is the set of minimum-cost pipelines satisfying multiple prefix-average conditional miscoverage constraints.
We introduce Coverage-Constrained Sequential Model Confidence Sets (CC-SMCS), which separate certifiably feasible, possibly feasible, and possibly constrained-optimal pipelines.
Using simultaneous martingale confidence sequences, CC-SMCS projects a rectangular confidence region onto the constrained argmin and admits an exact closed-form rule.
With probability at least $1-δ$, it contains every constrained-optimal pipeline simultaneously over all times.
This finite-sample guarantee requires no stationarity or mixing assumptions and remains valid under data-dependent stopping.
We also establish an impossibility result for safe certification at the coverage boundary and extend the construction to delayed multi-horizon feedback and outcome-dependent efficiency objectives.