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.
I thought how good the solution is is dependent on the utility function, not the optimisation process.
The objective function that measures the value of the solution should be a part of the problem: it's part of figuring out what counts as a solution in the first place. Maybe in some cases the solution is binary: if you're solving an equation, you either get a root or you don't.
In some cases, the value of solution is complicated to assess: how do you trade off a cure for cancer that fails in 10% of all cases, versus a cure for cancer that gives the patient a permanent headache? But either way you need an objective function to tell the AI (or the human) wha...
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.