# Re: Optimality of using probability

From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Mon Feb 05 2007 - 22:31:15 MST

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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