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YVLIAZ comments on MIRI's Approach - Less Wrong
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I think you are overhyping the PAC model. It surely is an important foundation for probabilistic guarantees in machine learning, but there are some serious limitations when you want to use it to constrain something like an AGI:
It only deals with supervised learning
Simple things like finite automata are not learnable, but in practice it seems like humans pick them up fairly easily.
It doesn't deal with temporal aspects of learning.
However, there are some modification of the PAC model that can ameliorate these problems, like learning with membership queries (item 2).
It's also perhaps a bit optimistic to say that PAC-style bounds on a possibly very complex system like an AGI would be "quite doable". We don't even know, for example, whether DNF is learnable in polynomial time under the distribution free assumption.
I would definitely call it an open research problem to provide PAC-style bounds for more complicated hypothesis spaces and learning settings. But that doesn't mean it's impossible or un-doable, just that it's an open research problem. I want a limitary theorem proved before I go calling things impossible.