用置信域评估局部更新风险，确保选择的更新有可靠改进保证。

How can training data be used to compare local updates to the current model, choose an update, and retain valid bounds for the selected update's population-risk change? We construct lower and upper confidence fields that jointly cover the population-risk change of every update in a possibly continuous local update space. The fields can therefore be used both to compare the updates and to select an update; a negative upper endpoint certifies improvement over the reference model. For linear risk changes in possibly infinite-dimensional feature spaces, cross-calibration uses the discrepancy between two balanced folds to calibrate the full-sample estimation error. Under covariance-aligned sub-Gaussian tails, covariance-estimation stability, and sufficient sample size, the cross-calibrated field has finite-sample simultaneous coverage. The confidence field's directional widths are governed by a population ridge effective dimension rather than the ambient feature dimension. For losses formed locally by continuous selection among finitely many smooth branches, separate uniform bounds for the linear Taylor field, Taylor remainder, and branch-interface discrepancy extend the field to every local update.