Sharper finite-budget guarantees

Derive sharper finite-budget performance guarantees for BMA-GAI and related budgeted multi-attribute verification methods, beyond the paper’s asymptotic coverage results.

Background

The paper establishes asymptotic coverage and first-order optimality results as the confidence level tends to zero with budgets scaled as logarithms of the inverse confidence level. These results characterize leading-order behavior but do not provide the sharpest finite-budget characterization.

The authors explicitly leave open the derivation of sharper finite-budget guarantees, which would quantify performance more precisely at practical budgets and account for lower-order terms, critical budget effects, and finite-sample certification behavior.