Sequential Certification of Partially Identified Product Targets: Information Limits and Adaptive Sampling
Abstract
We study the cost of certifying a scalar target driven by a product of centered Bernoulli means when an unobserved terminal gate leaves irreducible uncertainty. Each factor can be queried independently at a price. We derive the exact identified interval and determine when a requested accuracy is feasible. At every fixed strictly feasible interior instance, the optimal high-confidence expected cost is (1+o(1))log(1/δ)/D*, where D* is an answer-and-allocation information game; a globally honest procedure attains this benchmark. At product cancellation, we solve the game through a one-dimensional inverse-KL equation and explicit cost weights. For two tickets, quartic projections and rational bounds give checkable global optimality gaps. Joint confidence--precision limits expose a failure of the analyzed fixed pilot: it can cost asymptotically at least twice the optimum. A charged, precision-aware pilot with checkpoint certification restores optimal expected cost in exact arithmetic when log{e+log(1/g)}=o(log(1/δ)) for effective precision g, including exponential and certain double-exponential precision scales. Pooled rescue preserves validity and cannot increase observation cost on coupled paths. Implemented auditors verify returns by rational inequalities; reproducible experiments show both savings and finite-confidence overhead. These guarantees concern the specified independent-reference model and its scalar target.
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BibTeX
@misc{skiredj2026sequential,
title = {{Sequential Certification of Partially Identified Product Targets: Information Limits and Adaptive Sampling}},
author = {Abdallah Skiredj and Abderrahman Skiredj and Amal El Fallah Seghrouchni},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07567},
eprint = {2611.07567},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07567},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sequential Certification of Partially Identified Product Targets: Information Limits and Adaptive Sampling
AU - Abdallah Skiredj
AU - Abderrahman Skiredj
AU - Amal El Fallah Seghrouchni
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07567
UR - https://arxiv.org/abs/2611.07567
AB - We study the cost of certifying a scalar target driven by a product of centered Bernoulli means when an unobserved terminal gate leaves irreducible uncertainty. Each factor can be queried independently at a price. We derive the exact identified interval and determine when a requested accuracy is feasible. At every fixed strictly feasible interior instance, the optimal high-confidence expected cost is (1+o(1))log(1/δ)/D^*, where D^* is an answer-and-allocation information game; a globally honest procedure attains this benchmark. At product cancellation, we solve the game through a one-dimensional inverse-KL equation and explicit cost weights. For two tickets, quartic projections and rational bounds give checkable global optimality gaps. Joint confidence--precision limits expose a failure of the analyzed fixed pilot: it can cost asymptotically at least twice the optimum. A charged, precision-aware pilot with checkpoint certification restores optimal expected cost in exact arithmetic when log{e+log(1/g)}=o(log(1/δ)) for effective precision g, including exponential and certain double-exponential precision scales. Pooled rescue preserves validity and cannot increase observation cost on coupled paths. Implemented auditors verify returns by rational inequalities; reproducible experiments show both savings and finite-confidence overhead. These guarantees concern the specified independent-reference model and its scalar target.
ER -