> We therefore conclude that theoretically motivated experiment choice is potentially damaging for science, but in a way that will not be apparent to the scientists themselves.

They are analyzing a toy model of science. The details and in figure 1. They have a search space that has a few Gaussians like

f(x,y,z) = A0 * expt(-(x-x0)^2-(y-y0)^2-(z-z0)^2) + A1 * expt(-(x-x1)^2-(y-y1)^2-(z-z1)^2)

but maybe in more than 3 dimensions and maybe with more than 2 Gaussians.

They want the agents to find all of Gaussians.

It's somewhat similar to a maximization problem that is easier. There are many strategies for this, from gradient ascent to random sampling to a million more of variants. I like simulated annealing.

They claim that the best method is random sampling, that only work when the search space is small. But it breaks quite fast for high dimensional problems, unless the Gaussians are so big that cover most of the space, and perhaps I'm beeing too optimistic. Add noise, overlapping Gaussians and the problem gets super hard.

Let's get to a realistic example, all the molecules with 6 Carbons and 12 Hydrogens. Let's try to find all of them and their stables 3D configuration. This is chemistry from the first year in the university, perhaps earlier, no cutting edge science.

You have 18 atoms, so 18 * 3 = 54 dimensions, and the surface of -energy has a lot of mountains ranges and nasty stuff. Most of them very sharp. Let's try to find the local points of maximal -energy, that is much easier than the full map. These are the stable molecules, that (usually) have names.

* There is a cycle one with 6 Carbons, where each Carbon has 2 Hydrogens, https://en.wikipedia.org/wiki/Cyclohexane Note that it actually has two different 3D variants.

* There is one with a cycle of 5 Carbons and 1 carbon attached to the cycle https://en.wikipedia.org/wiki/Methylcyclopentane

* There are variants with shorter cycles, but I'm not sure how stable they are and Wikipedia has no page for them.

* There is also 3 linear versions, where the 6 Carbons are a s wavy line, and there is a double bound in one of the steps https://en.wikipedia.org/wiki/1-Hexene I'm not sure why the other two version have no page in Wikipedia, I think they should be stable, but sometimes it's not a local maximum or the local maximum is to shallow and the double bound jump and the Hydrogen reorganize.

* And there may be other nasty stuff, take a look at the complete list https://en.wikipedia.org/wiki/C6H12.

And don't try to make the complete list when of molecules that includes a few Nitrogen, because the number of molecules explodes exponentially.

So this random sampling method they propose, does not even work for an elementary Chemistry problem.

Can random experimental choice lead to better theories?