Generalization bounds for mixing processes via delayed online-to-PAC conversions

TL;DR

This paper establishes new generalization bounds for learning algorithms trained on data from stationary mixing processes by linking online learning with delayed feedback to statistical learning, revealing a trade-off between delay and dependence.

Contribution

It introduces an analytic framework connecting online learning with delayed feedback to generalization bounds for non-i.i.d. data from mixing processes, providing near-optimal rates.

Findings

Bounded regret online algorithms imply low generalization error in mixing data.

Trade-off between delay in online learning and data dependence affects rates.

Near-optimal bounds achieved when delay is tuned to mixing time.

Abstract

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.