We introduce the technique of generic chaining and majorizing measures for controlling sequential Rademacher complexity. We relate majorizing measures to the notion of fractional covering numbers, which we show to be dominated in terms of sequential scale-sensitive dimensions in a horizon-independent way, and, under additional complexity assumptions establish a tight control on worst-case sequential Rademacher complexity in terms of the integral of sequential scale-sensitive dimension. Finally, we establish a tight contraction inequality for worst-case sequential Rademacher complexity. The above constitutes the resolution of a number of outstanding open problems in extending the classical theory of empirical processes to the sequential case, and, in turn, establishes sharp results for online learning.

翻译：我们采用一般链锁和主要措施技术,以控制相继雷德马赫公司的复杂程度。我们把主要措施与分层覆盖数字的概念联系起来,我们以视地平线独立的方式表明,在顺序的敏感程度方面,我们以分层覆盖数字的概念为主导,在额外的复杂假设下,从顺序的敏感程度的一体化方面,严格控制最坏情况相继雷德马赫的复杂程度。最后,我们为最坏情况相继雷德马赫的复杂程度,建立了严格的收缩不平等。以上是将经验过程的经典理论扩展至相继案例方面一些悬而未决的问题的解决,反过来,又为在线学习取得显著成果。