As every school child knows, an advanced AI can be seen as an optimisation process - something that hits a very narrow target in the space of possibilities. The Less Wrong wiki entry proposes some measure of optimisation power:
One way to think mathematically about optimization, like evidence, is in information-theoretic bits. We take the base-two logarithm of the reciprocal of the probability of the result. A one-in-a-million solution (a solution so good relative to your preference ordering that it would take a million random tries to find something that good or better) can be said to have log2(1,000,000) = 19.9 bits of optimization.
This doesn't seem a fully rigorous definition - what exactly is meant by a million random tries? Also, it measures how hard it would be to come up with that solution, but not how good that solution is. An AI that comes up with a solution that is ten thousand bits more complicated to find, but that is only a tiny bit better than the human solution, is not one to fear.
Other potential measurements could be taking any of the metrics I suggested in the reduced impact post, but used in reverse: to measure large deviations from the status quo, not small ones.
Anyway, before I reinvent the coloured wheel, I just wanted to check whether there was a fully defined agreed upon measure of optimisation power.
Thanks for the links, but I don't understand your objections - when measuring the optimisation power of a system or an AI, costs such as cycles, memory use, etc... are already implicitly included in Eliezer's measure. If the AI spends all it's time calculating without ever achieving anything, or if it has too little memory to complete any calculations, it will achieve an optimisation of zero.
Can you make sense of Shane Legg's objection, then?
One of my criticisms was this:
I don't see the point of calling something "optimisation power" - and then using it to award a brain-dead algorithm full marks.
I think your objection shows that you failed to read (or appreciate) this bit:
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