We study the generalization error of statistical learning algorithms in a
non-i.i.d. setting, where the training data is sampled from a stationary mixing
process. We develop an analytic framework for this scenario based on a
reduction to online learning with delayed feedback. In particular, we show that
the existence of an online learning algorithm with bounded regret (against a
fixed statistical learning algorithm in a specially constructed game of online
learning with delayed feedback) implies low generalization error of said
statistical learning method even if the data sequence is sampled from a mixing
time series. The rates demonstrate a trade-off between the amount of delay in
the online learning game and the degree of dependence between consecutive data
points, with near-optimal rates recovered in a number of well-studied settings
when the delay is tuned appropriately as a function of the mixing time of the
process.

通过将训练数据从一个混合过程进行采样，我们研究了统计学习算法在非独立同分布的环境中的泛化误差，并基于延迟反馈的在线学习提出了一个分析框架。特别地，我们展示了即使数据序列是从混合时间序列采样得到的情况下，通过存在一个具有有界遗憾的在线学习算法（针对一个固定的统计学习算法，在一个特殊构建的延迟反馈的在线学习博弈中），所述统计学习方法的泛化误差较低。这些速率展示了在线学习博弈中的延迟量和连续数据点之间的依赖程度之间的权衡，当延迟适当地调整为过程的混合时间的函数时，可以在许多研究良好的情形下恢复近乎最优的速率。