How to measure optimisation power

Stuart_Armstrong

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.

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.

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.

Yudkowsky's attempt seems to be of little practical use - as I explain in the comments there and here. It's a combination of a not-very-useful concept and misleading terminology.

Legg's AIQ seems to be a much more reasonable approach. Mahoney has previously done something similar.

Related to Legg's work: Ben Goertzel's paper "Toward a Formal Characterization of Real-World General Intelligence "

Abstract:

Two new formal definitions of intelligence are presented, the ”pragmatic general intelligence” and ”efficient pragmatic general intelligence.” Largely inspired by Legg and Hutter’s formal definition of ”universal intelligence,” the goal of these definitions is to capture a notion of general intelligence that more closely models that possessed by humans and practical AI systems, which combine an element of universality with

... (read more)

1Stuart_Armstrong14y

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.

2gwern14y

I discussed a third group's attempt: http://lesswrong.com/lw/42t/aixistyle_iq_tests/

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How to measure optimisation power

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How to measure optimisation power

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