How does the world evolve as we take actions in the world?

leads to state S3.

An MDP consists of a set of states

Dehydrated.

Here is a diagram of the state space for the vacuum world.

And so we'll implement this Path Cost function, in terms of a Step Cost function.

Then the alpha, the learning rate, is 1 2. That gives us 45.

And suppose for now, every other state costs you 3.

So wherever you see a variable without a quantifier, assume that there's a For All.

So we wish to have a planning method that provides an answer no matter where we are and that's called a policy.

Narrator The next question is challenging.

And now we can start searching backwards.

Then we have situations, and situations are also objects in the logic, and they correspond not to states but rather to paths the paths of actions that we have in state space search.

Next, a function Actions that takes a state as input and returns a set of possible actions that the agent can execute when the agent is in this state.

We apply that 45 to the state action pair.

We seek to maximize a reward function that we define over states.

Norvig

In our route finding problem, the initial state was the agent being in the city of Arad.

And then, in addition to the transition, we need a reward function which we'll denote R.

We've learned about Markov Decision Processes.

And in general, a successor state axiom will have the form of saying for all actions and states, if it's possible to execute action A in state S, then and I'll show in general what they look like here the fluent is true if and only if action A made it true or action A didn't undo it.

And then we start branching on the possible actions, so say one possible action would be to load the cargo, C1, onto the plane, P1, at SFO, and then that would bring us to another state which would have a different set of state variables set, and we'd continue branching out like that until we hit a state which satisfied the goal predicate.

In some problems, the agent will have the same actions available in all states and in other problems, he'll have different actions dependent on the state.

We have a set of players P that can be our one player, as in this game, or two or more.

But you'll find a single sequence of actions and states that might cut the corners, as close as possible, to reach the plus 100 as fast as possible.

In each case, we'd be updating only the action we took, associated with that state, not the whole state.

S is an element of the state, S a set of actions

We have fully observable with a set of states and corresponding actions where they have stochastic action effects characterized by a conditional probability entity of P of S prime given that we apply action A in state S.

Status Loaded and running.

And what we say is our new belief state is the result of updating what we get from predicting what our action will do and then updating it, based on our observation, O, of the world.

So for example a policy might look as follows for this state, we wish to go north, north, east, east, east, but for this state over here, we wish to go north, maybe east over here, and maybe west over here.

Suppose you have states S1, S2, and S3, and you have actions A1 and A2.

And now instead of describing the actions that are applicable in a situation with a predicate Actions of S, situation calculus for some reason decided not to do that and instead we're going to talk about the actions that are possible in the state, and we're going to do that with a predicate.

Now let's expand it more, and there's now two options finally

So here's one example of a successor state axiom.

Let me tell you a little bit about this chemistry of oil.

So if the policy here was to go up and then go right, then we would always stick to that and the only time we would explore any other state is when those actions failed.

That's what we mean by deterministic, and so that means the size of the belief state will either stay the same or it might decrease if 2 of the actions sort of accidentally end up bringing you to the same place.

Just tell me how your team is progressing.

So here's a partial diagram of the part of the belief state from that world, and I want it to show how the belief state unfolds as 2 things happen.

Surpass the kinetic so they have enough kinetic energy to get into the activation state, and then they can go to the

These are used to describe what happens in the state that's a successor of executing an action.

Now the set of all of the states here is known as the state space, and we navigate the state space by applying actions.

Water in a solid state is called ice.

It's really different from planning than before because of the stochasticity of the action effects.