for more abstract domains, it’s harder to define a criterion (or set of criteria) that we want our optimizer to satisfy

Yes.

But there’s a significant difference between choosing an objective function and “defining your search space” (whatever that means), and the latter concept doesn’t have much use as far as I can see.

If you don’t know what it means, how do you know that it’s significantly different from choosing an “objective function” and why do you feel comfortable in making a judgment about whether or not the concept is useful?

In any case, to define a search space is to provide a spanning set of production rules which allow you to derive all elements in the target set. For example, Peano arithmetic provides a spanning set of rules for arithmetic computations, and hence define ( in one particular way ) the set of computations a search algorithm can search through in order to find arithmetic derivations satisfying whatever property. Similarly the rules of chess define the search-space for valid board-state sequences in games of chess. For neural networks, it could be defining a set of topologies, or a set of composition rules for layering networks together; and in a looser sense a loss function induces “search space” on network weights, insofar as it practically excludes certain regions of the error surface from the region of space any training run is ever likely to explore.

I honestly regret that I didn’t make it as clear as I possibly could the first time around, but expressing original, partially developed ideas is not the same thing as reciting facts about well-understood concepts that have been explained and re-explained many times. Flippancy is needlessly hostile.

If not wholly inapplicable, then not performant, yes. Though the problem isn’t that the search-space is not defined at all, but that the definitions which are easiest to give are also the least helpful ( to return to the previous example, in the Platonic real there exists a brainf*ck program that implements an optimal map from symptoms to diagnoses—good luck finding it ). As the original author points out, there’s a tradeoff between knowledge and the need for brute-force. It may be that you can have an agent synthesize knowledge by consolidating the results of a brute-force search into a formal representation which an agent can then use to tune or reformulate the search-space previously given to fit some particular purposes; but this is quite a level of sophistication above pure brute force.

Edit:

If the problems of literature or philosophy were not in some sense “ill posed” they would also be dead subjects. The ‘general’ part in AGI would seem to imply some capacity for dealing with vague, partially defined ideas in useful ways.