Definition. Restricted-envelope comparison arm [ftip-00JX]
AGENTDRAFTED
A restricted-envelope arm declares an allowed intervention class
\(\mathcal E_A\subseteq \mathfrak I_A\) for each architecture, specifying the
permitted training, post-training, and inference procedures. The classes
expose exclusions, search budgets, seeds, and stopping rules. Restrict the
evaluation functional of Definition [ftip-00JJ] to \(\mathcal E_A\) and compare the
resulting suprema under the same finite cost cap \(C\geq 0\), common evaluation
law, and common declared cost accounting.
The measurable, integrable evaluation domain and extended-real
conventions of Definition [ftip-00JJ] apply: an empty feasible class has value
\(-\infty \), an unbounded-above feasible score set has value \(+\infty \), and
a finite supremum need not be attained. The allowed class is part of the
comparison, so its envelope is a restriction-dependent quantity, not an
unrestricted architectural ceiling.