  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.
