Academian comments on Frequentist Magic vs. Bayesian Magic - Less Wrong

41 Post author: Wei_Dai 08 April 2010 08:34PM

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Comment author: SilasBarta 09 April 2010 03:43:40PM *  3 points [-]

Apparently, for every time and space bounds (t,l), Hutter has defined an algorithm AIXI(t,l) that performs optimally assuming "the environment is computable". Sounds like an awesome model to compare our own rationality against:

Meh. I was excited about it at first, but here's the problem: that claim, at least as you've phrased it, is wrong. It would only be correct if you mean average performance over all computable environments, having an Occamian prior as their only knowledge.

But if you consider agents that operate in this computable environment, there are numerous examples that perform better than AIXI-tl. Specifically, all animals do. The reason is that they don't, like AIXI/AIXI-tl, start from tabula rasa, but are born with implicit knowledge about their environments (that is closer to the truth than a mere Occamian prior) and implicit heuristics for exploiting them.

That's why Hutter isn't just running AIXI-tl and outfoxing them all. (pardon the pun)

More generally, there's the important issue that we shouldn't want an agent that performs optimally, on average, over all computable environments, if that means sacrificing performance in this environment, which it almost certainly does.

Comment author: Academian 09 April 2010 04:17:11PM *  1 point [-]

That's a good point; in-born priors are much better (as priors) for typical human environments, and plenty of environments we'd like to design robots for.

But consider things like black holes, the relativity of pretty much everything kinematic except light speed, and almost all of quantum mechanics. These theories stopped seeming like outright paradoxes to me precisely when I eased up and starting assuming only that the universe was probably just computational in some sense, and not necessarily "3D-physical" or "spacial" or "temporal" or whatever. So naturally, I'm pleased to find a well-developing theory of "AIXI", an idealized implementation of this very starting point :)