Marcus Hutter

I didn't explicitly talk about it, but this is used for universal prediction and plug it into the sequential decision tree mechanism.

And then you get the best of both worlds.

You have a long-term planning agent,

but it doesn't need to know anything about the world because the Solomon of Induction part learns.

So what it does is, in the simplest case, I said, take the shortest program describing your data, run it, have a prediction which would be deterministic.

Yes.

Okay.

But you should not just take the shortest program, but also consider the longer ones, but keep it lower a priori probability.

So in the Bayesian framework, you say a priori any distribution

which is a model or a stochastic program, has a certain a priori probability, which is 2 to the minus, and why 2 to the minus length, I could explain, length of this program.

So longer programs are punished a priori.

And then you multiply it with the so-called likelihood function, which is, as the name suggests, is how likely is this model given the data at hand.

So if you have a very wrong model, it's very unlikely that this model is true.

And so it is very small number.

So even if the model is simple, it gets penalized by that.

And what you do is then you take just the sum or this is the average over it.

And this gives you a probability distribution.

So it's universal distribution or Solomon of distribution.

It's a basic optimization problem.

What are we talking about?