# Re: Optimality of using probability

From: Tennessee Leeuwenburg (tennessee@tennessee.id.au)
Date: Mon Feb 05 2007 - 23:20:40 MST

Bayesian reasoning seems straightforward enough. Assuming it's the best
method of reasoning, perhaps each agent doesn't need tailored reasoning
abilities, but rather a tailored ontology.

Cheers,
-T

On 2/6/07, Eliezer S. Yudkowsky <sentience@pobox.com> wrote:
>
> Mitchell Porter wrote:
> >
> > If you the programmer ('you' being an AI, I assume) already have the
> > concept of probability, and you can prove that a possible program will
> > estimate probabilities more accurately than you do, you should be able
> > to prove that it would provide an increase in utility, to a degree
> > depending on the superiority of its estimates and the structure of
> > your utility function. (A trivial observation, but that's usually where
> > you have to start.)
>
> Mitch, I haven't found that problem to be trivial if one seeks a precise
> demonstration. I say "precise demonstration", rather than "formal
> proof", because formal proof often carries the connotation of
> first-order logic, which is not necessarily what I'm looking for. But a
> line of reasoning that an AI itself carries out will have some exact
> particular representation and this is what I mean by "precise". What
> exactly does it mean for an AI to believe that a program, a collection
> of ones and zeroes, "estimates probabilities" "more accurately" than
> does the AI? And how does the AI use this belief to choose that the
> expected utility of running its program is ordinally greater than the
> expected utility of the AI exerting direct control? For simple cases -
> where the statistical structure of the environment is known, so that you
> could calculate the probabilities yourself given the same sensory
> observations as the program - this can be argued precisely by summing
> over all probable observations. What if you can't do the exact sum?
> How would you make the demonstration precise enough for an AI to walk
> through it, let alone independently discover it?
>
> *Intuitively* the argument is clear enough, I agree.
>
> --
> Eliezer S. Yudkowsky http://intelligence.org/
> Research Fellow, Singularity Institute for Artificial Intelligence
>

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