发表机构
Sichuan University; Southwestern University of Finance and Economics（四川大学; 西南财经大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究在标量高斯因果实验中量化了学习修复与评估目标间的差距，提出前导对数前沿并证明诊断弃权规则在未知参数下达到最优评估指数，揭示了目标依赖的信息需求变化。
AI 中文摘要
了解因果预测器可能改进的程度并不一定能揭示实际学习到的修复所获得的增益。我们在一个具有已知干预几何结构的标量高斯因果实验中量化了这一差距：辅助数据在有限污染范围内识别效应大小，而诊断则识别方向。目标是已实现训练修复相对于拟合参考的平方损失增益。在统一学习MSE $\eta$ 下联合优化学习器和评估器，避免了不进行修复的平凡解。在通常的$1/k$学习尺度下，每个可行的学习器都面临$k^{-2}$的评估下限，即使预言机潜力能以更快的速率估计。在幅度丰富机制中，我们刻画了一个尖锐的前导对数前沿：评估指数在相对首阶上为$\min{\ell_k,2k\eta_k/U}$，其中$\ell_k=\log(1/(k^2E_k))$，$E_k$为辅助精度。一种诊断弃权（不执行）规则在未知烦扰参数下达到该指数。我们还限制了关键允许窗口，并通过精确高斯模拟将前沿转移到自适应采样。有限网格实验区分了符号尾部抑制与总MSE，并暴露了保守的有限预算行为。该结果隔离了评估目标如何改变此实验中的信息需求；这不是一般的因果可识别性声明。
英文摘要
Knowing how much a causal predictor could improve need not reveal the gain of the repair actually learned. We quantify this gap in a scalar Gaussian causal experiment with known intervention geometry: auxiliary data identify effect magnitude up to bounded contamination, while diagnostics identify direction. The target is the squared-loss gain of the realized trained repair relative to a fitted reference. Jointly optimizing the learner and assessor under uniform learning MSE $η$ avoids the trivial solution of making no repair. At the usual $1/k$ learning scale, every feasible learner incurs a $k^{-2}$ assessment floor, even when oracle potential is estimable at a faster rate. In the magnitude-rich regime, we characterize a sharp leading-log frontier: the assessment exponent is $\min{\ell_k,2kη_k/U}$ to first relative order, where $\ell_k=\log(1/(k^2E_k))$ and $E_k$ is auxiliary precision. A diagnostic-abstention rule attains this exponent with unknown nuisance parameters. We also bound the critical allowance window and transfer the frontier to adaptive sampling by exact Gaussian simulation. Finite-grid experiments distinguish sign-tail suppression from total MSE and expose conservative finite-budget behavior. The result isolates how the assessment target changes information requirements in this experiment; it is not a general causal identifiability claim.
