The bound is the same one you get for normal Solomonoff induction, except restricted to the set of programs the cut-off induction runs over. It’s a bound on the total expected error in terms of CE loss that the predictor will ever make, summed over all datapoints.
Look at the bound for cut-off induction in that post I linked, maybe? Hutter might also have something on it.
Can also discuss on a call if you like.
Note that this doesn’t work in real life, where the programs are not in fact restricted to outputting bit string predictions and can e.g. try to trick the hardware they’re running on.
Yeah I know that bound, I’ve seen a very similar one. The problem is that mesa-optimisers also get very good prediction error when averaged over all predictions. So they exist well below the bound. And they can time their deliberately-incorrect predictions carefully, if they want to survive for a long time.
The bound is the same one you get for normal Solomonoff induction, except restricted to the set of programs the cut-off induction runs over. It’s a bound on the total expected error in terms of CE loss that the predictor will ever make, summed over all datapoints.
Look at the bound for cut-off induction in that post I linked, maybe? Hutter might also have something on it.
Can also discuss on a call if you like.
Note that this doesn’t work in real life, where the programs are not in fact restricted to outputting bit string predictions and can e.g. try to trick the hardware they’re running on.
Yeah I know that bound, I’ve seen a very similar one. The problem is that mesa-optimisers also get very good prediction error when averaged over all predictions. So they exist well below the bound. And they can time their deliberately-incorrect predictions carefully, if they want to survive for a long time.