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

Published: 18 Dec 2024, Last Modified: 14 Feb 2025ALT 2025EveryoneRevisionsBibTeXCC BY 4.0
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.
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Submission Number: 101
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