What ML algorithms can be used to optimize or find the maximum?

Question

Neural networks

Machine learning is not my specialty, so I stuck a little on such a question. In general, many libraries usually have a train function that takes input and a result. Further, this function tries to select the weights so that the neural network produces the desired result on the corresponding data. Thus, the task of classification is performed. Okay, I've got this figured out.

But what if I don't have a set with the expected results? Is there some function that gives an estimate (better-worse or bad-good, in general, it doesn’t matter) and I need to adjust the weights of the neural network so that the estimate is as high as possible? Let it be as an example - the passage of a platformer. I have a simple function that gives a score based on how fast and how far the character got to a point.

I kind of understand that some kind of genetic algorithm is needed here, which will mutate the weights of the neural network. And I can't google specific libraries. Therefore, I would like the name of specific libs that implement this approach. Well, or at least keywords for which you can google this topic.

neataptic seemed to be what I needed, but I started digging, and the resulting set is also needed there. Or I just didn’t find how to transfer something like a fitness function here.