Online Learning and Disambiguations of Partial Concept Classes

Authors Tsun-Ming Cheung, Hamed Hatami, Pooya Hatami, Kaave Hosseini

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Tsun-Ming Cheung
  • McGill University, Montreal, Canada
Hamed Hatami
  • McGill University, Montreal, Canada
Pooya Hatami
  • Ohio State University, Columbus, OH, USA
Kaave Hosseini
  • University of Rochester, NY, USA


We wish to thank Mika Göös for clarifying the reductions in [Bousquet et al., 2014; Göös, 2015; Göös et al., 2016; Balodis et al., 2022].

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Tsun-Ming Cheung, Hamed Hatami, Pooya Hatami, and Kaave Hosseini. Online Learning and Disambiguations of Partial Concept Classes. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 42:1-42:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


In a recent article, Alon, Hanneke, Holzman, and Moran (FOCS '21) introduced a unifying framework to study the learnability of classes of partial concepts. One of the central questions studied in their work is whether the learnability of a partial concept class is always inherited from the learnability of some "extension" of it to a total concept class. They showed this is not the case for PAC learning but left the problem open for the stronger notion of online learnability. We resolve this problem by constructing a class of partial concepts that is online learnable, but no extension of it to a class of total concepts is online learnable (or even PAC learnable).

Subject Classification

ACM Subject Classification
  • Theory of computation → Online learning theory
  • Online learning
  • Littlestone dimension
  • VC dimension
  • partial concept class
  • clique vs independent set
  • Alon-Saks-Seymour conjecture
  • Standard Optimal Algorithm
  • PAC learning


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