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gwern comments on Rationality Quotes May 2012 - Less Wrong
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There might well be a theorem formalising that statement. There might also be one formalising the statement that every remotely optimal form of induction or decision-making is uncomputable. If that's the way it is, well, that's the way it is.
This is an argument of the form "Suppose X were true -- then X would be true! So couldn't X be true?"
You try to find a method that solves enough examples of the NP-hard problem well enough to sell the solutions, such that your more bounded ambition puts you back in the realm of P. This is done all the time -- freight scheduling software, for example. Or airline ticket price searching. Part of designing optimising compilers is not attempting analyses that take insanely long.
Harder classes are subsets of NP-hard, and everything in NP-hard is hard enough to make the point. Of course, there is the whole uncomputability zoo above all that, but computing the uncomputable is even more of a wild goose chase. "Omega flies up to you and hands you a box containing the Secrets of Immortality; for every digit of Chatin's Omega you correctly type in, you get an extra year, and it stops working after the first wrong answer".
No, this is pointing out that if you provide an optimal outcome barricaded by a particular obstacle, then that optimal outcome will trivially be at least as hard as that obstacle.
This is exactly the point made for computable approximations to AIXI. Thank you for agreeing.
Are you sure you want to make that claim? That all harder classes are subsets of NP-hard?
Fantastic! I claim my extra 43 years of life.
No, carelessness on my part. Doesn't affect my original point, that schemes for approximating Solomonoff or AIXI look like at least exponential brute force search.
Since AIXI is, by construction, the best possible intelligent agent, all work on AGI can, in a rather useless sense, be described as an approximation to AIXI. To the extent that such an attempt works (i.e. gets substantially further than past attempts at AGI), it will be because of new ideas not discovered by brute force search, not because it approximates AIXI.
43 years is a poor sort of immortality.
Well, yeah. Again - why would you expect anything else? Given that there exist problems which require that or worse for solution? How can a universal problem solver do any better?
Yes.
No. Given how strange and different AIXI works, it can easily stimulate new ideas.
It's more than I had before.
The spin-off argument. Here's a huge compendium of spinoffs of previous approaches to AGI. All very useful, but not AGI. I'm not expecting better from AIXI.
Hm, so let's see; you started off mocking the impossibility and infeasibility of AIXI and any computable version:
Then you admitted that actually every working solution can be seen as a form of SI/AIXI:
And now you're down to arguing that it'll be "very useful, but not AGI".
Well, I guess I can settle for that.
I stand by the first quote. Every working solution can in a useless sense be seen as a form of SI/AIXI. The sense that a hot-air balloon can be seen as an approach to landing on the Moon.
At the very most. Whether AIXI-like algorithms get into the next edition of Russell and Norvig, having proved of practical value, well, history will decide that, and I'm not interested in predicting it. I will predict that it won't prove to be a viable approach to AGI.
How can a hot air balloon even in theory be seen as that? Hot air has a specific limit, does it not - where its density equals the outside density?