IDENTIFICATION IS NOT REWARD: DISCOVERING TRAINING FEASIBILITY BOUNDARIES

A successful hyperparameter search finds configurations that train well, but may reveal little about where training ceases to be feasible. We study how to recover this boundary from a fixed budget of short runs and turn it into a usable learning-rate scale. Our approach fits a finite grammar of threshold models, selects experiments through template disagreement, and compiles the fitted boundary into a schedule. The protocol evaluates boundary identification and collected-run reward separately. A threshold-identification analysis explains why reward-optimal sampling can leave the boundary unidentified, while monotone inversion connects an identified cut to a control scale. On synthetic tasks, active discovery recovers planted cuts to the reported precision while reward-seeking Bayesian optimization achieves higher sample reward. On CIFAR-10, the same protocol improves identification in harder proxy-label settings and supports a separate sharpness-based feasibility probe. Under label-noise stress, compiled scales improve over hand-set cosine schedules; a scale-by-shape comparison attributes the improvement primarily to the scale. These results establish a practical route from short-run experiments to explicit, actionable descriptions of training feasibility.