Here’s an idea for a modification of Solomonoff induction that no longer has a subjectively-chosen machine to encode hypotheses in. One could instead simply consider how many bits it would take to encode a solution on all universal Turing machines, and making each hypotheses’ prior equal to the average of its prior on each machine. This makes somewhat intuitive sense, as one doesn’t know which “machine” the universe in “programmed” on, so it’s best to just assume a random machine. Unless I’m mistaken, there’s an infinite number of universal Turing machines, but I think algorithms could still approximate the induction.
Here’s an idea for a modification of Solomonoff induction that no longer has a subjectively-chosen machine to encode hypotheses in. One could instead simply consider how many bits it would take to encode a solution on all universal Turing machines, and making each hypotheses’ prior equal to the average of its prior on each machine. This makes somewhat intuitive sense, as one doesn’t know which “machine” the universe in “programmed” on, so it’s best to just assume a random machine. Unless I’m mistaken, there’s an infinite number of universal Turing machines, but I think algorithms could still approximate the induction.
How would you take the average over an infinite number of UTM’s? You would first need to choose a distribution on them.