Supervising the Deployed Prediction in Finite Context Adaptation

Context-adapted dynamics models deploy predictions fitted to observed support; perturbation training can instead supervise the midpoint of predictions fitted to altered supports. We ask when this supervision choice changes learning beyond allowed hyperparameter retuning. At fixed disagreement regularization, finite-step adaptation lets midpoint supervision compensate or amplify learning bias. Under smoothness assumptions, we bound prediction changes outside allowed tuning directions; a two-mode example establishes exact separation from any shared scalar penalty. Across three settings from two dynamics families, central supervision reduces error relative to midpoint supervision by 3.61-4.12% in matched comparisons and 2.52-2.71% after independent retuning under the primary noisy-support protocol. Using prediction responses to select an objective reduces equal-budget error by 1.90% relative to fixed centered transfer-noise regularization and 1.51% relative to one-probe central consistency, charging online selection but excluding reusable development calibration. Supervision placement matters for learning and objective choice under computational budgets.