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

2024-06-18

arXiv.org

AI Summary

This paper investigates the impact of stationary, mixing time-series data under non-i.i.d. conditions on the generalization error of statistical learning. Addressing the challenge of strong temporal dependence among training samples, we propose a novel framework that reduces non-i.i.d. learning to online learning with delayed feedback—marking the first integration of delayed online learning with PAC-style generalization analysis. Our theoretical analysis uncovers a fundamental trade-off between the delay parameter and the mixing time, yielding near-optimal generalization bounds. The method applies broadly to β-, φ-, and α-mixing processes, delivering tight, verifiable generalization guarantees even under strong temporal dependence. As a result, it significantly enhances the theoretical reliability and practical applicability of statistical learning algorithms for time-series data.

Technology Category

• Machine Learning: Online Learning & Bandits
• Natural Language Processing: Learning & Optimization for NLP
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Social networks and social learning
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Generalization error in non-i.i.d. settings
• Online learning with delayed feedback
• Trade-off between delay and data dependence

Innovation

• Online learning with delayed feedback
• Generalization error in non-i.i.d.
• Trade-off between delay and dependence