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I know it's generally considered bad form to add another answer on top of an accepted one, but this one is by special request and it's a topic that deserves its own discussion. The topic is: Effective learning algorithms vs. learning rules. A learning rule is simply a mathematically well-defined mapping from a labeled sample to some function class. (The ...


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There has been a recent line of work on computable learnability: http://proceedings.mlr.press/v117/agarwal20b/agarwal20b.pdf http://www.learningtheory.org/colt2021/virtual/static/images/agarwal21b.pdf This seems to be exactly the sort of thing you're asking about. You also ask about the implications $1\implies 2$ and $2\implies 3$. The latter is indeed ...


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