The IMP game

Learnability, approximability and adversarial learning beyond Σ1

Michael Brand, David L. Dowe

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We introduce a problem set-up we call the Iterated Matching Pennies (IMP) game and show that it is a powerful framework for the study of three problems: adversarial learnability, conventional (i.e. non-adversarial) learnability and approximability. Using it, we are able to derive the following theorems. (i) It is possible to learn by example all of σ1 1 as well as some supersets; (ii) in adversarial learning (which we describe as a pursuit-evasion game), the pursuer has a winning strategy (in other words, σ1 can be learned adversarially, but 0 1 not); (iii) some languages in σ1 cannot be approximated by any language in σ1. In particular, we show that some languages that are not computable are nevertheless learnable by example. We show corresponding results also for σi and 0 i for arbitrary i.

Original languageEnglish
Pages (from-to)2171-2192
Number of pages22
JournalJournal of Logic and Computation
Volume27
Issue number7
DOIs
Publication statusPublished - 1 Oct 2017

Keywords

  • adversarial learning
  • approximability
  • approximation
  • decidable
  • elusive model paradox
  • halting
  • halting problem
  • learnability
  • matching pennies
  • Nash equilibrium
  • recursively enumerable
  • red herring sequence
  • Turing machine

Cite this

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title = "The IMP game: Learnability, approximability and adversarial learning beyond Σ1",
abstract = "We introduce a problem set-up we call the Iterated Matching Pennies (IMP) game and show that it is a powerful framework for the study of three problems: adversarial learnability, conventional (i.e. non-adversarial) learnability and approximability. Using it, we are able to derive the following theorems. (i) It is possible to learn by example all of σ1 1 as well as some supersets; (ii) in adversarial learning (which we describe as a pursuit-evasion game), the pursuer has a winning strategy (in other words, σ1 can be learned adversarially, but 0 1 not); (iii) some languages in σ1 cannot be approximated by any language in σ1. In particular, we show that some languages that are not computable are nevertheless learnable by example. We show corresponding results also for σi and 0 i for arbitrary i.",
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The IMP game : Learnability, approximability and adversarial learning beyond Σ1. / Brand, Michael; Dowe, David L.

In: Journal of Logic and Computation, Vol. 27, No. 7, 01.10.2017, p. 2171-2192.

Research output: Contribution to journalArticleResearchpeer-review

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T2 - Learnability, approximability and adversarial learning beyond Σ1

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AU - Dowe, David L.

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KW - matching pennies

KW - Nash equilibrium

KW - recursively enumerable

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