Population-Preserving Loss Corrections for Finite-Sample Decision Selection

Losses with identical population comparisons can select different decisions from finite samples. We study shared loss corrections learned across tasks and deployed by empirical minimization over fixed candidate banks. Conditionally centered controls preserve population preferences while changing joint empirical comparisons. We characterize harmful selection through multivariate Chernoff bounds, an entropy dual, and a convex-reference support certificate for zero regret. Regularized exponential construction in a reproducing kernel Hilbert space has a finite positive-cone representation, but convex comparison criteria admit an unbounded multiplicative gap to decision risk, even for bounded losses and one correction parameter. Direct episodic welfare fitting over a $d$-parameter affine family instead achieves excess risk of order $\sqrt{d\log (2M)/N}$ from $N$ independent tasks with at most $M$ candidates, without a margin assumption. A centered sensor construction gives a matching $\sqrt{d/N}$ lower bound for fixed bank size, even when each sampled task's law is revealed. Independent validation adds finite-library oracle and baseline-safety guarantees. Controlled sensor and contextual studies examine functional capacity, joint comparison information, and the difference between convex construction and direct decision-risk fitting.