Statistical learning theory under independent and identically distributed (iid) sampling and online learning theory for worst case individual sequences are two of the best developed branches of learning theory. Statistical learning under general non-iid stochastic processes is less mature. We provide two natural notions of learnability of a function class under a general stochastic process. We show that both notions are in fact equivalent to online learnability. Our results are sharpest in the binary classification setting but we also show that similar results continue to hold in the regression setting.

翻译：在独立和相同分布的统计学习理论(二d) 最坏个案个人序列的抽样和在线学习理论是最先进的学习理论的两个分支。在一般非二类随机程序下的统计学习不那么成熟。我们提供了在一般随机程序下功能类学习的两个自然概念。我们表明这两个概念事实上等同于在线学习。我们的结果在二进制分类设置中最为尖锐,但我们也表明类似的结果在回归设置中依然有效。