发表机构
Imperial College London（帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明偏好压缩界是紧的，通过均匀分布和次序统计量的显式构造在极限下达到该界，并给出更简洁的证明。
AI 中文摘要
缺乏严格的安全与性能证书仍然是现代基于学习方法部署的关键瓶颈。样本压缩最近成为推导此类证书的强大工具，特别是对于满足所谓偏好性质（在学习理论文献中也称为稳定性）的算法，可获得尤为尖锐的界。这些界直接应用于情景方法、选择学习和支持向量方法等不同领域。然而，这些界是否紧仍是一个未解问题。在本文中，我们肯定地回答了这个问题，并证明最先进的偏好压缩界是可证明紧的。我们通过基于均匀分布和次序统计量的显式构造来确立这一点，该构造在极限情况下达到该界。在此过程中，我们还提供了该界的一个更短且更易理解的证明，仅需要基本的计数论证，无需无限维对偶。
英文摘要
The lack of rigorous safety and performance certificates remains a key bottleneck to the deployment of modern learning-based methods. Sample compression has recently emerged as a powerful tool for deriving such certificates, with particularly sharp bounds available for algorithms satisfying a so-called preference property -- also known as stability in the learning theory literature. These bounds find direct application across domains as different as the Scenario Approach, Pick-to-Learn, and Support Vector methods. However, whether they are tight has remained an open problem. In this paper we resolve this question affirmatively and show that the state-of-the-art bound for preferent compressions is provably tight. We establish this by exhibiting an explicit construction based on the uniform distribution and order statistics that attains the bound in the limit. Along the way, we also provide a considerably shorter and more accessible proof of this bound, requiring only elementary counting arguments and no infinite-dimensional duality.
Comments14 pages, 6 figures, to appear at the 65th IEEE Conference on Decision and Control (CDC 2026)
