We provide a novel dimension-free uniform concentration bound for the empirical risk function of constrained logistic regression. Our bound yields a milder sufficient condition for a uniform law of large numbers than conditions derived by the Rademacher complexity argument and McDiarmid's inequality. The derivation is based on the PAC-Bayes approach with second-order expansion and Rademacher-complexity-based bounds for the residual term of the expansion.

翻译：本文针对约束逻辑回归的经验风险函数，提出了一种新颖的维度无关一致浓度界。相较于基于Rademacher复杂性论证和McDiarmid不等式导出的条件，该界为一致大数定律提供了更宽松的充分条件。推导过程基于PAC-Bayes方法，结合二阶展开技术，并对展开余项使用基于Rademacher复杂性的界进行控制。