We’re flipping a coin. If you think the coin is biased with unknown bias, but flips are otherwise independent, then you expect to see more of what we’ve already got. Eliezer calls it anti-Occamian to expect less of what we’ve already got—to invert Laplace’s rule of succession.
This is still a simple rule for assigning probabilities. But what about the Turing machines? Even if you start out by assuming that TMs in the family “look at the average pattern so far, then use some noise to usually against it continuing” have high prior probability, if the pattern really does hold then they must grow in complexity linearly faster than the hypothesis family “use some noise to usually bet with the average pattern,” because of the growth rates of the different required “noise.”
In order to prevent your favored “anti-Occamian” pattern from ever being overtaken, you’d have to penalize competing hypotheses superexponentially for their length (so that for no bias of the coin does a competing hypothesis win). This is a drastic measure that basically destroys Solomonoff induction and replaces it with a monoculture.
Let me look at the toy example just for fun:
We’re flipping a coin. If you think the coin is biased with unknown bias, but flips are otherwise independent, then you expect to see more of what we’ve already got. Eliezer calls it anti-Occamian to expect less of what we’ve already got—to invert Laplace’s rule of succession.
This is still a simple rule for assigning probabilities. But what about the Turing machines? Even if you start out by assuming that TMs in the family “look at the average pattern so far, then use some noise to usually against it continuing” have high prior probability, if the pattern really does hold then they must grow in complexity linearly faster than the hypothesis family “use some noise to usually bet with the average pattern,” because of the growth rates of the different required “noise.”
In order to prevent your favored “anti-Occamian” pattern from ever being overtaken, you’d have to penalize competing hypotheses superexponentially for their length (so that for no bias of the coin does a competing hypothesis win). This is a drastic measure that basically destroys Solomonoff induction and replaces it with a monoculture.