Just before we start, I've just been notified of a major innovation in IT at FAU.

The camera now follows me.

Yesterday was the first time they told me that they're doing it now and they like it.

Apparently I'm one of the professors who runs around most while teaching, so they use me as a guinea pig.

There you see it. If you get seasick, you probably have to complain.

Okay, and now it's time to start.

So remember what we're trying to do in the next week is to build agents that can deal with uncertainty in their world model.

Last semester we had agents that were certain about the world state by making unreasonable assumptions like

asymptomism and fully observable environments.

Okay, we want to lift those.

So we need to go from agents that keep track of a single state to agents that track belief states, sets of states.

And since we have uncertainty, we have to model likelihood and all of those kind of things because we want to make good predictions about the world.

And it makes a difference whether this possible world has a likelihood of 1% and the other one of 99%.

If we treat them equal, then we're not doing everything optimal.

So we have to do something that allows our agents to deal with uncertainty.

Now, one thing that you want to realize in this is we're not dealing with uncertainty because the world is somehow uncertain.

No.

Right?

It is snowing in downtown Erlangen or it isn't.

We just don't know.

Okay, so the agent doesn't know, which isn't because the world is somehow fishy.

The world is still crisp and clear.

But the agent doesn't know because they're not there or they don't have a phone connection or whatever.

Okay, so that's the reason we're looking at uncertainty.

And we're going to build up the math for that.

And we've started doing that.

So which means we're going to do probability theory and we're going to do a relatively simple probability theory,

discrete probability theory with an eye towards doing computation with it in the real world.

So we really care for the computational overhead and the modeling overhead we have to do to actually work with these things.

Because if we want to build the agents, we have to know all these probabilities, which is quite a lot of data.

And if our agent tries to optimize whether to jump left or to jump right while the truck is driving at it,

if it takes an hour, the agent is dead before it notices that, oh, I should go left.

Sometimes we have to have time and computational constraints and take them into account.

So the first thing we're going to look into and there are two problems to solve here.

One is to have models of a world that we're uncertain about.

And then another distinct problem is to take decisions about optimal actions based on this.

Those are completely different things.

We're only going to do the first one first.

Later, we're going to do things like modeling rationality by maximizing expected utility.

Different story, OK?

One we're completely doing without today and in the next week.

And we've already looked at the basics of probability theory.

Basically, what is probability?

We have a sample space, the underlying one, right?

And we have a probability measure that assigns any subset of the probability space,

of the outcome space with a number between 0 and 1.

We sometimes use percentages for that.

And we have certain restrictions on that function P.

It has to have the right summation and universality properties.

And if we have that, we can work with this.