Tim, when I said relative to a space I did not mean relative to its size. This is clear in my example of a hill topography, where increasing the scale of the hill does not make it a qualitatively different problem, just move to positions that are higher will work. In fact, the whole motivation for my suggestion is the realization that the structure of that space is what limits the results of a given optimizer. So it is relative to all the properties of the space that the power of an optimizer should be defined, to begin with. I say begin with because there are many other technical difficulties left, but i think that measures of power for optimizers that operate on different spaces do not compare meaningfully.
Tim, when I said relative to a space I did not mean relative to its size. This is clear in my example of a hill topography, where increasing the scale of the hill does not make it a qualitatively different problem, just move to positions that are higher will work. In fact, the whole motivation for my suggestion is the realization that the structure of that space is what limits the results of a given optimizer. So it is relative to all the properties of the space that the power of an optimizer should be defined, to begin with. I say begin with because there are many other technical difficulties left, but i think that measures of power for optimizers that operate on different spaces do not compare meaningfully.
Sure—you aren’t making the same mistake as the original poster in that department.
Comparing to the size of the search space is pretty daft—since the search space is often unbounded in optimisation problems.