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So I should write down some other things first, just to ground the notations, but what I’ll do is eventually come up with an algorithm for computing V*, the optimal value function and then we’ll plug them into this and that will give us the optimal policy p*.

And so I’ll write down the algorithm in a second, but just to ground the notation, well – yeah, let’s skip that. Let’s just talk about the algorithm. So this is an algorithm called value iteration and it makes use of Bellman’s equations for the optimal policy to compute V*. So here’s the algorithm. Okay, and that’s the entirety of the algorithm and oh, you repeat the step, I guess. You repeatedly do this step.

So just to be concrete, let’s say in my MDP of 11 states, the first step is initialize V(s) equals zero, so what that means is I create an array in computer implementation, create an array of 11 elements and say set all of them to zero. Says I can initialize into anything. It doesn’t really matter.

And now what I’m going to do is I’ll take Bellman’s equations and we’ll keep on taking the right hand side of Bellman’s equations and overwriting and start copying down the left hand side. So we’ll essentially iteratively try to make Bellman’s equations hold true for the numbers V(s) that are stored along the way. So V(s) here is in the array of 11 elements and I’m going to repeatedly compute the right hand side and copy that onto V(s).

And it turns out that when you do this, this will make V(s) converge to V*(s), so it may be of no surprise because we know V* [inaudible] set inside Bellman’s equations.

Just to tell you, some of these ideas that they get more than the problem says, so I won’t prove the conversions of this algorithm. Some implementation details, it turns out there’s two ways you can do this update. One is when I say for every state s that has performed this update, one way you can do this is for every state s, you can compute the right hand side and then you can simultaneously overwrite the left hand side for every state s. And so if you do that, that’s called a sequence update. Right and sequence [inaudible], so update all the states s simultaneously.

And if you do that, it’s sometimes written as follows. If you do synchronous update, then it’s as if you have some value function, you’re at the Ith iteration or Tth iteration of the algorithm and then you’re going to compute some function of your entire value function, and then you get to set your value function to your new version, so simultaneously update all 11 values in your s space value function.

So it’s sometimes written like this. My B here is called the Bellman backup operator, so the synchronized valuation you sort of take the value function, you apply the Bellman backup operator to it and then the Bellman backup operator just means computing the right hand side of this for all the states and you’ve overwritten your entire value function.

The only way of performing these updates is asynchronous updates, which is where you update the states one at a time. So you go through the states in some fixed order, so would update V(s) for state No. 1 and then I would like to update V(s) for state No. 2, then state No. 3, and so on. And when I’m updating V(s) for state No. 5, if V(s) prime, if I end up using the values for states 1, 2, 3, and 4 on the right hand side, then I’d use my recently updated values on the right hand side. So as you update sequentially, when you’re updating in the fifth state, you’d be using values, new values, for states 1, 2, 3, and 4. And that’s called an asynchronous update.

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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.
Bharti
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
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
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
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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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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