aiqbench analysis
This research introduces a rigorous statistical framework using prequential e-values to certify near-optimality in sequential black-box optimization, addressing the common pitfall of tuning Gaussian process envelopes adaptively without compromising validity. By filtering out contradicted candidates from a predeclared set, the method ensures anytime-valid guarantees while significantly reducing false-certification risks compared to standard fit-then-certify approaches. This advancement strengthens the theoretical foundations for reliable hyperparameter optimization and safe stopping rules in machine learning workflows.
Prequential E-Values for Selected-GP Near-Optimality Certificates
arXiv:2609.39123v1 Announce Type: new Abstract: 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.
Abstract: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.
9 pages, 2 figures. Accepted at the NeurIPS 2026 Workshop on E-Values: From Statistics to ML
Machine Learning (cs.LG)
arXiv:2609.39123 [cs.LG]
(or arXiv:2609.39123v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.39123 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 313 words
