At great risk of sounding completely ignorant, this approach is basically what I thought the point of machine learning was - cleverly using feedback loops to improve things automatically. The thing that sticks out to me as particularly cool about FunSearch is the use of programs as inputs/outputs and the fact that they managed to automate feedback.

I'm pretty naive in terms of granular understanding here as I am barely proficient in Python, to be clear, but when I daydream about things you could solve with machine learning/AI, this is the approach I always think of and I guess is how I thought it already worked. Load it up with the best information we have currently, define the desired results as clearly as possible, implement some form of automatic feedback, and let it run iteratively until it produces something better than what you had before.

Is this a case of "well no shit, but actually implementing that effectively is the hard part"? Is it being able to quickly apply it to a wide variety of problems? I guess I'm trying to understand whether this is a novel idea (and if so, what parts are novel), or if the idea has been around and it's a novel implementation.