Yes! Sometimes you know that a solution will take a particular mathematical form, without knowing what the parameters will be. So you can write down a program (

Yes! Sometimes you know that a solution will take a particular mathematical form, without knowing what the parameters will be. So you can write down a program (function) that can express any solution of that form, and use an optimization algorithm e.g. gradient descent on labeled examples, to figure out which specific instance of your possible solutions works best.