Dah. Hang on, what am I talking about- chess has a finite number of moves so the "language" is finite. That means it's learnable in polynomial time, from finite examples ... in principle :)
Right, but even if chess were infinite, we could still imagine an algorithm that would output the smallest explicit rule set that was consistent with all the games it had seen so far, and that would quickly (though how quickly?) converge on the correct rules in the case of chess, even if it would be up against undecidability when trying to do the same thing for a completely arbitrary game.
It depends on how you mean "converge". It would certainly tend towards the full ruleset, learning more of them, or more accurate versions of them, the more examples it saw. It would not really terminate though, at least according to the learnability results from inductive inference.
Results from inductive inference show that you’re not going to converge in general. In the specific case of chess, however, my point was that we, because we know the complete list of rules, could plausibly look in from the outside and say after some finite point: “ah yes, now the system has gotten all of them.”
Oh, I see. Yes, for sure. That'd be the active learning framework [1]. I get the feeling it's not very popular because it inserts a human in the process. Many machine learning people are rather allergic to anything that a) introduces "human bias" to the learning process and b) reduces the potential for end-to-end automation.
The article you quoted above is a good example. It's main claim is that an evaluation function was learned without knowledge of rules or hand-crafted features, i.e. explicit human participation.
It's a political issue, really. And a silly one- there are domains where very useful background knowledge is available; physics, language, mathematics, etc. There's no reason not to use it.
In chess, for example, it might be possible to learn a decent set of rules just by carefuly choosing the examples to feed to the learner. Or, indeed, evaluating the learning so-far, therefore acting as an all-knowing Oracle.
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[1] Well, strictly speaking active learning is where the system asks the user for examples/ counterexamples, but there's different options and what you suggest would fit in there.
