发表机构
Eindhoven University of Technology; University of Amsterdam（埃因霍温理工大学; 阿姆斯特丹大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对高维置信序列紧致性与计算效率的矛盾，提出基于投注的投资组合区域的可处理外部近似，兼顾紧致性与统计有效性，并显著优于现有方法。
AI 中文摘要
现代序贯监控问题常涉及多个指标，我们同时监控多个数据流，并可能在证据足够强时采取行动。置信序列（CSs）是此类连续监控的自然工具。然而，对于有界向量均值，现有的多元置信序列要么紧致但计算上不可处理，要么计算快速但保守。为解决这一问题，我们研究了基于一维投注的置信序列向高维的三种提升方式：加权Bonferroni区域、等价的极大财富形式以及投资组合区域。投资组合区域通常更为紧致，尤其是在高维情况下，但其边界及体积等属性没有闭式解。为使这一更紧致的构造可用，我们提出了投资组合区域的可处理外部近似，并保持统计有效性：一个边界框、一个$\ell_p$-椭球体以及它们的交集。我们证明了所有构造之间的集合关系，并通过实验表明这些近似（i）能达到接近不可处理投资组合的区域，（ii）显著优于现有的可处理多元置信序列，（iii）支持如多指标A/B测试和模型比较等实际应用场景。
英文摘要
Modern sequential monitoring problems often involve multiple metrics, where we monitor several data streams simultaneously and may act once the evidence is strong enough. Confidence sequences (CSs) are a natural tool for such continuous monitoring. However, for bounded vector means, existing multivariate CSs are either tight but computationally intractable, or fast to compute but conservative. To address this, we study three lifts of one-dimensional betting-based CSs to higher dimensions: a weighted Bonferroni region, an equivalent max-wealth form, and a portfolio region. The portfolio is typically much tighter, especially in higher dimensions, but its boundary and properties such as volume are not available in closed form. To make this tighter construction usable, we propose tractable outer approximations of the portfolio region that preserve statistical validity: a bounding box, an $\ell_p$-ellipsoid, and their intersection. We prove set relations among all constructions and show empirically that these approximations (i) achieve regions close to the intractable portfolio, (ii) substantially outperform existing tractable multivariate CSs, and (iii) enable practical use cases such as multi-metric A/B testing and model comparison.
CommentsAccepted at NeurIPS 2026 (Spotlight)
