用于所选GP近最优性证书的先验E值
Prequential E-Values for Selected-GP Near-Optimality Certificates
浏览论文内容
中文总结 AI 辅助
提出基于先验E值的可审计GP停止规则，通过在线测试候选包络并保留有效上界，在保持功效的同时显著降低错误认证风险。
中文摘要 AI 辅助
在顺序优化昂贵的黑箱函数时，如超参数优化，我们可能希望在最佳评估值被证明在全局最优的$\varepsilon$范围内时停止。这样的证书需要两个要素：所选值的下置信界和定义域上的上置信包络，通常由高斯过程（GP）提供。当定义此包络的核和常数在运行前固定时，GP-UCB风格的停止规则是有效的，但实际诱惑是从相同的自适应评估中调整包络，然后像固定一样进行认证。我们使用先验E值使这种选择可审计：从一个预先声明的完全指定的GP/RKHS包络集合开始，每个候选者通过其自身的一步超前E过程进行测试，被反驳的候选者被删除，认证使用幸存者中的最大上界。通过有效的所选点下界和一个声明的候选者具有有效的潜在覆盖和噪声校准，该规则是任意时间有效的。在512个种子的噪声RBF应力扫描中，与先拟合后认证相比，它在相当的功效下将错误认证风险大致减半。相对于在光滑的$d=3,4$目标上随机固定的GP预承诺，每个额外的错误证书分别伴随着3.0和13.5个额外的正确证书。
英文摘要
When optimizing an expensive black-box function sequentially, as in hyperparameter optimization, we may want to stop once the best evaluated value is certified within $\varepsilon$ of the global optimum. Such a certificate needs two ingredients: a lower confidence bound for the selected value and an upper confidence envelope over the domain, typically supplied by a Gaussian process (GP). GP-UCB-style stopping rules are valid when the kernel and constants defining this envelope are fixed before the run, but the practical temptation is to tune the envelope from the same adaptive evaluations and then certify as if it had been fixed. We use prequential e-values to make this selection auditable: starting from a predeclared set of fully specified GP/RKHS envelopes, each candidate is tested by its own one-step-ahead e-process, contradicted candidates are deleted, and certification uses the largest upper bound among the survivors. With a valid selected-point lower bound and one declared candidate having valid latent coverage and noise calibration, the rule is anytime-valid. On a 512-seed noisy RBF stress sweep, it roughly halves false-certification risk at comparable power versus fit-then-certify. Relative to random fixed GP precommitment on smooth $d=3,4$ objectives, each additional false certificate is accompanied by 3.0 and 13.5 additional correct certificates, respectively.
发表机构
- Meta Platforms（Meta平台）
机构由 AI 辅助整理，请以论文原文为准。
