Whenever you’re picking a program to do a task, you run into similar constraints as when you’re trying to pick a program to make predictions. There an infinite number of programs, so you can’t just put a uniform prior on which one is best, you need some way of ranking them. Simplicity is a ranking. Therefore, ranking them by simplicity works, up to a constant. The induction problem really does seem similar—the only difference is that in prediction, the cost function is simple, but in action, the cost function can be complicated.
I don’t have a copy of Li and Vitanyi on me at the moment, but I wonder if they have anything on how well SI does if you have a cost function that’s a computable function of prediction errors.
Whenever you’re picking a program to do a task, you run into similar constraints as when you’re trying to pick a program to make predictions. There an infinite number of programs, so you can’t just put a uniform prior on which one is best, you need some way of ranking them. Simplicity is a ranking. Therefore, ranking them by simplicity works, up to a constant. The induction problem really does seem similar—the only difference is that in prediction, the cost function is simple, but in action, the cost function can be complicated.
I don’t have a copy of Li and Vitanyi on me at the moment, but I wonder if they have anything on how well SI does if you have a cost function that’s a computable function of prediction errors.