The IMP game: Learnability, approximability and adversarial learning beyond Σ1

Michael Brand, David L. Dowe

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    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
    Issue number7
    Publication statusPublished - 1 Oct 2017


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

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