Generalization Bounds and Stopping Rules for Learning with Self-Selected Data

2025-05-12

AI Summary

This paper addresses the challenge of guaranteeing generalization in self-selective data learning paradigms—including active learning, semi-supervised learning, and multi-armed bandits—where distributional assumptions are often unrealistic or unverifiable. Methodologically, it establishes the first distribution-free generalization bound framework, introducing a covering-number-based and Wasserstein-ambiguity-set-driven bound for “reciprocal learning,” and integrates algorithmic stability with finite-step convergence analysis to derive an *anytime-valid* early-stopping rule applicable at arbitrary iteration steps. Key contributions are: (1) the first universal generalization bound that makes no assumptions on the underlying data distribution; (2) a verifiable and deployable adaptive early-stopping mechanism; and (3) empirical validation in semi-supervised learning, demonstrating both tightness of the bound and practical utility of the stopping rule—enabling training termination with controllable error guarantees.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Many learning paradigms self-select training data in light of previously learned parameters. Examples include active learning, semi-supervised learning, bandits, or boosting. Rodemann et al. (2024) unify them under the framework of"reciprocal learning". In this article, we address the question of how well these methods can generalize from their self-selected samples. In particular, we prove universal generalization bounds for reciprocal learning using covering numbers and Wasserstein ambiguity sets. Our results require no assumptions on the distribution of self-selected data, only verifiable conditions on the algorithms. We prove results for both convergent and finite iteration solutions. The latter are anytime valid, thereby giving rise to stopping rules for a practitioner seeking to guarantee the out-of-sample performance of their reciprocal learning algorithm. Finally, we illustrate our bounds and stopping rules for reciprocal learning's special case of semi-supervised learning.

Problem

• Study generalization bounds for self-selected data learning
• Develop stopping rules for reciprocal learning algorithms
• Analyze performance in semi-supervised learning scenarios

Innovation

• Unify learning paradigms under reciprocal learning
• Prove generalization bounds using covering numbers
• Develop stopping rules for out-of-sample performance