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So it turns out that there’s a version of Bellman’s equations for V* as well and so this is also called Bellman’s equations for V* rather than for Vp and I’ll just write that down. So this says that the optimal payoff you can get from the state s is equal to – so our [inaudible] are multi here, so let’s see. Just for starting off in the state s, you’re going to get your immediate R(s) and then depending on what action a you take your expected total payoff will be given by this. So if I take an action a in some state s, then with probability given by P subscript (s; a) of s prime, by this probability our transition of state s prime, and when we get to the state s prime, I’ll expect my total payoff from there to be given by V*(s) prime because I’m now starting to use the s prime.

So the only thing in this equation I need to fill in is where is the action a, so in order to actually obtain the optimal expected payoff, and to actually obtain the maximum or the optimal expected total payoff, what you should choose here is the max over our actions a, choose your action a that maximizes the expected value of your total payoffs as well.

So it just makes sense. There’s a version of Bellman’s equations for V* rather than Vp and I’ll just say it again. It says that my optimal expected total payoff is my immediate reward plus, and then the best action it can choose, the max over all actions a of my expected future payoff.

And these also lead to my definition of p*, which is let’s say I’m in some state s and I want to know what action to choose. Well, if I’m in some state s, I’m gonna get here an immediate R(s) anyway, so what’s the best action for me to choose is whatever action will enable me to maximize the second term, as well as if my robot is in some state s and it wants to know what action to choose, I want to choose the action that will maximize my expected total payoff and so p*(s) is going to define as R(max) over actions a of this same thing.

I could also put the gamma there, but gamma is just a positive. Gamma is almost always positive, so I just drop that because it’s just a constant scale you go through and doesn’t affect the R(max).

And so, the consequence of this definition is that p* is actually the optimal policy because p* will maximize my expected total payoffs.

Cool. Any questions at this point? Cool. So what I’d like to do now is talk about how algorithms actually compute high start, compute the optimal policy. I should write down a little bit more before I do that, but notice that if I can compute V*, if I can compute the optimal value function, then I can plug it into this equation and then I’ll be done. So if I can compute V*, then you are using this definition for p* and can compute the optimal policy.

So my strategy for computing the optimal policy will be to compute V* and then plug it into this equation and that will give me the optimal policy p*. So my goal, my next goal, will really be to compute V*.

But the definition of V* here doesn’t lead to a nice algorithm for computing it because let’s see – so I know how to compute Vp for any given policy p by solving that linear system equation, but there’s an exponentially large number of policies, so you get 11 states and four actions and what the number of policies is froze to the par of 11. This is of a huge space of possible policies and so I can’t actually exhaust the union of all policies and then take a max on [inaudible].

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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
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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