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This is awesome. I was working on something similar (but got distracted) except my strategy was evolutionary. The idea was that the LLM had to figure out what it’s optimizing for itself.

I find that as soon as an LLM has an explicit definition of what it’s doing, the exploration/exploitation ratio swerves into exploitation and it gets stuck

This is very nicely done and much more clear to follow than the paper. One question: Does LLM get to evaluate the code using tool or guess the return value of f(x)?
Thanks! The LLM only sees the result of f(x). So like in the code writing example, the code is actually executed with `eval()`.