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Main Authors: Kalociński, Dariusz, Steifer, Tomasz
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2510.18352
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author Kalociński, Dariusz
Steifer, Tomasz
author_facet Kalociński, Dariusz
Steifer, Tomasz
contents Understanding when learning is possible is a fundamental task in the theory of machine learning. However, many characterizations known from the literature deal with abstract learning as a mathematical object and ignore the crucial question: when can learning be implemented as a computer program? We address this question for universal online learning, a generalist theoretical model of online binary classification, recently characterized by Bousquet et al. (STOC'21). In this model, there is no hypothesis fixed in advance; instead, Adversary -- playing the role of Nature -- can change their mind as long as local consistency with the given class of hypotheses is maintained. We require Learner to achieve a finite number of mistakes while using a strategy that can be implemented as a computer program. We show that universal online learning does not imply computable universal online learning, even if the class of hypotheses is relatively easy from a computability-theoretic perspective. We then study the agnostic variant of computable universal online learning and provide an exact characterization of classes that are learnable in this sense. We also consider a variant of proper universal online learning and show exactly when it is possible. Together, our results give a more realistic perspective on the existing theory of online binary classification and the related problem of inductive inference.
format Preprint
id arxiv_https___arxiv_org_abs_2510_18352
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Computable universal online learning
Kalociński, Dariusz
Steifer, Tomasz
Machine Learning
Logic in Computer Science
Understanding when learning is possible is a fundamental task in the theory of machine learning. However, many characterizations known from the literature deal with abstract learning as a mathematical object and ignore the crucial question: when can learning be implemented as a computer program? We address this question for universal online learning, a generalist theoretical model of online binary classification, recently characterized by Bousquet et al. (STOC'21). In this model, there is no hypothesis fixed in advance; instead, Adversary -- playing the role of Nature -- can change their mind as long as local consistency with the given class of hypotheses is maintained. We require Learner to achieve a finite number of mistakes while using a strategy that can be implemented as a computer program. We show that universal online learning does not imply computable universal online learning, even if the class of hypotheses is relatively easy from a computability-theoretic perspective. We then study the agnostic variant of computable universal online learning and provide an exact characterization of classes that are learnable in this sense. We also consider a variant of proper universal online learning and show exactly when it is possible. Together, our results give a more realistic perspective on the existing theory of online binary classification and the related problem of inductive inference.
title Computable universal online learning
topic Machine Learning
Logic in Computer Science
url https://arxiv.org/abs/2510.18352