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Choosing features for approximating the value function is often somewhat harder, so because the value of a state is how good is starting off in this state. What is my expected sum of discounted rewards? What if I start in a certain state? And so what the feature of the state have to measure is really how good is it to start in a certain state? And so for inverted pendulum you actually have that states where the poles are vertical and when a cart that’s centered on your track or something, maybe better and so you can come up with features that measure the orientation of the pole and how close you are to the center of the track and so on and those will be reasonable features to use to approximate V*. Although in general it is true that choosing features, the value function approximation, is often slightly trickier than choosing good features for linear regression.

Okay and then Justin’s questions of so given V*, how do you go back to actually find a policy? In the discrete case, so we have that ?*(s) is equal to all [inaudible] over A of that. So that’s again, I used to write this as a sum over states [inaudible]. I’ll just write this as an expectation and so then once you find the optimal value function V*, you can then find the optimal policy ?* by computing the [inaudible]. So if you’re in a continuous state MDP, then you can’t actually do this in advance for every single state because there’s an infinite number of states and so you can’t actually perform this computation in advance to every single state.

What you do instead is whenever your robot is in some specific state S is only when your system is in some specific state S like your car is at some position orientation or your inverted pendulum is in some specific position, posed in some specific angle T. It’s only when your system, be it a factor or a board game or a robot, is in some specific state S that you would then go ahead and compute this augmax, so it’s only when you’re in some state S that you then compute this augmax, and then you execute that action A and then as a result of your action, your robot would transition to some new state and then so it’ll be given that specific new state that you compute as augmax using that specific state S that you’re in.

There’re a few ways to do it. One way to do this is actually the same as in the inner loop of the fitted value iteration algorithm so because of an expectation of a large number of states, you’d need to sample some set of states from the simulator and then approximate this expectation using an average over your samples, so it’s actually as inner loop of the value iteration algorithm. So you could do that. That’s sometimes done. Sometimes it can also be a pain to have to sample a set of states to approximate those expectations every time you want to take an action in your MDP.

Couple of special cases where this can be done, one special case is if you have a deterministic simulator. If it’s a deterministic simulator, so in other words, if your similar is just some function, could be a linear or a nonlinear function. If it’s a deterministic simulator then the next state, ST+1, is just some function of your previous stated action. If that’s the case then this expectation, well, then this simplifies to augmax of A of V* of F of I guess S,A because this is really saying S prime=F(s),A. I switched back and forth between notation; I hope that’s okay. S to denote the current state, and S prime to deterministic state versus ST and ST+1 through the current state. Both of these are sorta standing notation and don’t mind my switching back and forth between them. But if it’s a deterministic simulator you can then just compute what the next state S prime would be for each action you might take from the current state, and then take the augmax of actions A, basically choose the action that gets you to the highest value state.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Machine learning. OpenStax CNX. Oct 14, 2013 Download for free at http://cnx.org/content/col11500/1.4
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