We've been looking at actions in our decision theory that actually only affect the, if you

want to see it that way, environment outside the agent. We're actually giving some kind

of a tablet or something, some kind of medicine to the patient. That's not realistic. Doctors

often do other stuff. They say, I can't decide on a treatment yet. I have to run a couple

of extra tests. I have to put you into the magnetic resonance thingamajig to see whether

there are any blocked arteries or something like this. So that is kind of an action that

doesn't really change the outside world or the patient, but really changes the network

because it gives us more information, more evidence, or takes certain, takes certain

variabilities out of the system. If we say, well, I have to first look whether there's

actually tachypnea or not, right? This is an easy diagnosis. That would actually give

us a concrete value and give us, give the CPT down here one less dimension. That might

actually help me quite a lot. The question now is, do I need to, should I do a test or

not? One of the most important things in decision making is to know when you need more information

because tests can be expensive, they can be hazardous, and they cost time. So if somebody,

somebody's dying directly, you better do something even if you don't really know what it is.

Because if you run a test that takes three hours, your patient will be dead anyway. So

it doesn't matter. So that is something we want to look at after the break. It's called

information value theory, namely, when should we do, when should we gather more information

to make better decisions? When does it pay? The idea now is that we understand how we

measure the utility of external actions, namely the actions that directly affect the world.

And you should, you should realize that is, that is the only thing people have, can have,

can have real preferences on. They don't really care. You think about it. They don't really

care of how good the doctors or diagnosis system internal workings are. They really

only want the optimal treatment. They don't even really care about the treatment either.

They only want to feel good afterwards. So the information value, the value of gathering

more information only indirectly comes into the utility. Okay? So we need a new theory

for that and that's called information value theory. And that actually brings us closer

to kind of changing worlds. So right now we only have, we have the assumption that the

world around us doesn't change. And when I say world around that, that's inaccurate

because the environment actually includes all of the agent itself. So we really enter

here a very simple form of sequential decision making because if I take, if I choose an information

gathering action that will only, that will not actually have a direct effect on the treatment.

You delay in a way the utility. And that's a bit of a problem for what I'm going to tell

you about. And we would need methods for that that we can actually, that will only start

tomorrow. But I would like to kind of lump the information value theory in here even

though there are some problems. Okay. And I want to have you consider the following

example. Okay. So we have the problem of buying all oil drilling rights. You get the right

to drill a deep hole somewhere and you hope that there's oil somewhere down there. If

there is, you can get, you can keep the oil, but for the right of drilling this hole, you

have to pay. And typically you kind of get a little piece of land you can drill on and

every piece of land costs a certain amount. And you typically don't know whether your

land has oil or not. And now the question is, should I just take the gamble or should

I pay somebody to do a survey first? These people who explode things and then measure

the seismic waves and then interpret there might be oil down there. Okay. So that's the

example. We have N blocks of rights and to make things simple, exactly one of them has

oil which has a worth of K. And so we have prior probabilities that says since we know

nothing the chance that a given plot has oil is one over N, of course, because there's

N and many of those and say that's mutually exclusive. It's not realistic, but that makes

our math easy. Okay. And say the current price of each block is K over N. That's the maximum

price you can ask and which is why the person who has that is going to ask that. So say