标题： 简单而精确的提升泛化界 显示英文标题

标题： Simple and Sharp Generalization Bounds via Lifting

摘要： 我们开发了一个信息论框架，用于界定随机过程的期望上确界和尾部概率，为泛化界限提供了比经典链式和分层论证更简单且更精确的替代方法。 关键思想是一个提升论证，它产生了经验过程界限的信息论类比，例如Dudley的熵积分。 提升引入了对称性，即使经典的Dudley积分较松散时也能得到精确的界限。 作为副产品，我们得到了主要测度定理的简洁证明，并提供了显式的常数。 信息论方法在泛化理论中提供了经典局部复杂度界限的软版本，但更为简洁，不需要分层论证。 我们将这种方法应用于Sobolev椭球和弱$\ell_q$球上的经验风险最小化，得到了更精确的收敛速率或扩展到经典方法未涵盖的设置。 显示英文摘要

摘要： We develop an information-theoretic framework for bounding the expected supremum and tail probabilities of stochastic processes, offering a simpler and sharper alternative to classical chaining and slicing arguments for generalization bounds. The key idea is a lifting argument that produces information-theoretic analogues of empirical process bounds, such as Dudley's entropy integral. The lifting introduces symmetry, yielding sharp bounds even when the classical Dudley integral is loose. As a by-product, we obtain a concise proof of the majorizing measure theorem, providing explicit constants. The information-theoretic approach provides a soft version of classical localized complexity bounds in generalization theory, but is more concise and does not require the slicing argument. We apply this approach to empirical risk minimization over Sobolev ellipsoids and weak $\ell_q$ balls, obtaining sharper convergence rates or extensions to settings not covered by classical methods.