I would love to see a more rigorous way to measure optimization power. It's a very important concept, and in fact we probably care more about optimization power than intelligence. On some days I'd rather talk about the possibility of an "optimization power explosion" than an "intelligence explosion."
I don't think a formalization has been made. I think Carl once suggested we might define optimization power in terms of capacity to achieve narrow goals across a canonical set of environments, but that's a long way from a formalization.
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:
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.