从投影观测出发认证分布鲁棒决策的方法研究
Certifying Distributionally Robust Decisions from Projection Observations
AI 导读
arXiv 论文提出仅凭标量观测即可认证鲁棒决策的方法：在有限高斯投影实验中，观测规律定义一组不可区分的矩模型，作者给出可返回决策或未决结果的置信集证书，并证明其可靠性及对不可区分模型必要弃判的性质。标量 profile 将非线性风险比较化为凸内层问题，七个合成实例中联合校准的矩区域给出比显式期望样本信息下界高 21 到 52 倍的充分预算，1900 条模拟流零决策错误；但保证依赖高斯复制。
正文 · 原文
Abstract:A scalar measurement can determine a robust decision without identifying the latent covariance or every decision risk. We study finite Gaussian projection experiments with a fixed mean-plus-standard-deviation target. The observation laws define a set of indistinguishable moment models. We exhibit decisions that agree throughout that set despite unidentified risk values, and give a confidence-set certificate that returns a decision or an unresolved outcome. We prove soundness, necessary abstention for indistinguishable models with incompatible optima, and a fixed-checkpoint certification guarantee. A scalar profile reduces nonlinear risk comparisons to convex inner problems. Across seven synthetic instances, jointly calibrated moment regions give sufficient budgets 21 to 52 times explicit expected-sample information lower bounds. Separately measured stopping times are lower, with zero decision errors in 1,900 simulated streams. These comparisons do not constitute matching bounds, and the guarantees require Gaussian replication.
| Subjects: | Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Optimization and Control (math.OC) |
| Cite as: | arXiv:2610.34493 [stat.ML] |
| (or arXiv:2610.34493v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.34493 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Pouya Ahadi [view email]
[v1]
Sun, 25 Oct 2026 18:37:26 UTC (37 KB)
来源：arXiv cs.AI · arxiv.org