Perhaps I'm not understanding it correctly, but here's my take on what the paper is doing.
Imagine you have a problem you want to solve (let's say, identify an OCR'd handwritten character, e.g. the MNIST Dataset). You tell 3 agents "Hey, each of you take a stab at getting really good at recognizing characters from this dataset. You can take 10 refinement steps to continue to improve ". You can't give each agent unlimited steps of course, because you have a finite amount of compute.
So each agent goes off, and by the end, Agent 1 got to 90% accuracy, Agent 2 got to 80% accuracy, and Agent 3 got to 89% accuracy. Agent 1 wins, of course.
But then you look at the refinement steps, and after 2 steps, Agent 1 was _already at_ 90% accuracy. So the agent spent the next 8 steps basically not moving at all. Agent 3 on the other hand, perhaps was continuously climbing in accuracy at every refinement step, but hit step 10 and had to stop.
Now because you recorded every step from every agent, you know what you'd do differently next time -- you'd not allocate as many steps to Agent 1, and give Agent 3 more steps, because perhaps that might result in Agent 3 coming up with a better answer.
From my understanding, that's what they built in the form of a "search" controller -- a way to evaluate automatically and reapply how you could allocate resources more effectively, when applied to a new problem.
But I guess my misunderstanding is how applicable the search controller is when applied to new problems -- just because one pathway stalled early for one problem, doesn't mean it would work for another?