Marcus Hutter

The world is not always adversarial.

So it can be, if there are other humans, even cooperative.

Or nature is usually, I mean, the dead nature is stochastic.

Things just happen randomly or don't care about you.

So what you have to take into account is the noise and not necessarily adversariality.

So you replace the minimum on the opponent's side by an expectation.

which is general enough to include also adversarial cases.

So now instead of a minimax strategy, you have an expectimax strategy.

So far so good, so that is well known, it's called sequential decision theory.

But the question is, on which probability distribution do you base that?

If I have the true probability distribution, like say I play Begaman, right?

There's dice and there's certain randomness involved.

I can calculate probabilities and feed it in the expectimax or the sequential decision tree, come up with the optimal decision if I have enough compute.

But for the real world, we don't know that.

What is the probability the driver in front of me brakes?

I don't know.

So it depends on all kinds of things, and especially new situations, I don't know.

So this is this unknown thing about prediction, and there's where Solomonov comes in.

So what you do is in sequential decision tree, you just replace the true distribution, which we don't know,

by this universal distribution.